Stochastic Programming Bibliography

Maarten H. van der Vlerk Department of Operations University of Groningen PO Box 800, NL-9700 AV Groningen, The Netherlands E-mail: [email protected] October 8, 2007

One of the sources for this bibliography has been the list of books on Stochastic Programming compiled by J. Dupacovˇ a,´ which can be found in Wets and Ziemba [4033]. Please send additions (preferably in BibTeX format) or comments to the e-mail address mentioned above. This bibliography can be cited as Maarten H. van der Vlerk. Stochastic Programming Bibliography. World Wide Web, http://mally.eco.rug.nl/spbib.html, 1996-2007. The BibTex entry I use is @MISC{SPB9607, author = {Maarten H. {van der Vlerk}}, title = {Stochastic Programming Bibliography}, year = {1996-2007, howpublished = {World Wide Web, \url{http://mally.eco.rug.nl/spbib.html}} } where the macro \url is deﬁned in the LATEX style ﬁle url.sty.

References

[1] I.N. Kamal Abadi, Nicholas G. Hall, and Chelliah Sriskandarajah. Minimizing cycle time in a blocking ﬂowshop. Oper. Res., 48(1):177–180, 2000. [2] J. Abaffy and E. Allevi. A modiﬁed L-shaped method. J. Optim. Theory Appl., 123(2):255–270, 2004. [3] Moncef Abbas and Fatima Bellahcene. Cutting plane method for multiple objective stochastic integer linear programming. European J. Oper. Res., 168(3):967–984, 2006. [4] N. E. Abboud, M. Y. Jaber, and N. A. Noueihed. Economic lot sizing with the consideration of random machine unavailability time. Comput. Oper. Res., 27(4):335–351, 2000. [5] P. Abel. Decisions in stochastic linear programming models under partial information. Z. Angew. Math. Mech. 73, No.7-8, T 737-T 738, 1993. [6] Peter Abel. Stochastische Optimierung bei partieller Information, volume 96 of Mathematical Systems in Economics. Verlagsgruppe Athenaum/Hain/Hanstein,¨ Konigstein/Ts.,¨ 1984.

1 [7] Peter Abel. Stochastic linear programming with recourse under partial information. In Probability and Bayesian statistics (Innsbruck, 1986), pages 1–6. Plenum, New York, 1987. [8] Peter Abel and Reiner Thiel. Mehrstuﬁge stochastische Produktionsmodelle. Eine praxisorientierte Darstellung mit programmierten Beispielen. Schriften zur Quantitativen Wirtschaftsforschung, Bd. 5. Frankfurt am Main: Rita G. Fischer Verlag., 1981. [9] Jinane Abounadi, Dimitri P. Bertsekas, and Vivek Borkar. Stochastic approximation for nonexpan- sive maps: application to Q-learning algorithms. SIAM J. Control Optim., 41(1):1–22 (electronic), 2002. [10] L.M. Abramov and I.I. Bockareva.ˇ A stochastic programming problem with probabilistic constraints. Optimal. Planirovanie, 16:3–9, 1970. [11] G.M. Adamenko. Solution of extremal problems under conditions of incomplete information. Automat. Control Comput. Sci., 14(4):48–55, 1980. [12] M. Ju. Afanas’ev. An example of the cycling of a stochastic integer algorithm in a bilevel multicommodity problem. In Methods of function analysis in mathematical economics (Russian), pages 111–114. Izdat. “Nauka”, Moscow, 1978. [13] P. K. Agarwal, B. K. Bhattacharya, and S. Sen. Improved algorithms for uniform partitions of points. Algorithmica, 32(4):521–539, 2002. [14] R.A. Agnew and R.B. Hempley. Finite statistical games and linear programming. Naval Res. Logist. Quart. 18, 99-102, 1971. [15] Saligrama Agnihothri, Uday S. Karmarkar, and Peter Kubat. Stochastic allocation rules. Oper. Res. 30, 545-555, 1982. [16] G.A. Agranovich and L.N. Kanov. A method of computing the gradient and the Hessian of the quality criterion in parametric optimization of continuous-discrete stochastic systems. J. Math. Sci., 82(3):3412–3415, 1996. Dynamical systems, No. 13. [17] S.C. Agrawal. On mixed integer quadratic programs. Naval Res. Logist. Quart., 21:289–297, 1974. [18] Vipul Agrawal and Sridhar Seshadri. Distribution free bounds for service constrained .Q; r/ inventory systems. Naval Res. Logist., 47(8):635–656, 2000. [19] C.C. Agunwamba. Optimality condition: constraint regularization. Math. Programming, 13(1):38– 48, 1977. [20] Rudolf Ahlswede and Ingo Wegener. Search problems. (Zadachi poiska). Transl. from the German. Moskva: Mir., 1982. [21] S. Ahmed and N. V. Sahinidis. Robust process planning under uncertainty. Industrial & Engineer- ing Chemistry Research, 37(5):1883–1892, 1998. [22] Shabbir Ahmed. Mean-risk objectives in stochastic programming. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [23] Shabbir Ahmed. Convexity and decomposition of mean-risk stochastic programs. Math. Program., 106(3, Ser. A):433–446, 2006. [24] Shabbir Ahmed. Smooth minimization of two-stage stochastic linear programs. Optimization Online, http://www.optimization-online.org, 2006. [25] Shabbir Ahmed, Ulas Cakmak, and Alexander Shapiro. Coherent risk measures in inventory problems. Stochastic Programming E-Print Series, http://www.speps.org, 2006.

2 [26] Shabbir Ahmed, Alan J. King, and Gyana Parija. A multi-stage stochastic integer programming approach for capacity expansion under uncertainty. Stochastic Programming E-Print Series, http://www.speps.org, 2001. [27] Shabbir Ahmed, Alan J. King, and Gyana Parija. A multi-stage stochastic integer programming approach for capacity expansion under uncertainty. Optimization Online, http://www. optimization-online.org, 2001. [28] Shabbir Ahmed and Alexander Shapiro. The sample average approximation method for stochastic programs with integer recourse. Optimization Online, http://www. optimization-online.org, 2002. [29] Shabbir Ahmed, Mohit Tawarmalani, and Nikolaos V. Sahinidis. A finite branch-and-bound algorithm for two-stage stochastic integer programs. Math. Program., 100(2, Ser. A):355–377, 2004. [30] Shabbir Ahmed, Mohit Tawarmalani, and Nikolas V. Sahinidis. A finite branch and bound algorithm for two-stage stochastic integer programs. Stochastic Programming E-Print Series, http://www.speps.org, 2000. [31] Byong-Hun Ahn and Bo-Woo Nam. Multiperiod optimal power plant mix under demand uncertainty. J. Oper. Res. Soc. Jap. 31, No.3, 353-370, 1988. [32] M. Aicardi, G. Casalino, F. Davoli, R. Minciardi, and R. Zoppoli. A decentralized closed-loop solution to the routing problem in networks. Annu. Rev. Autom. Program. 13, Part 2, 9-17, 1986. [33] Z.Zh. Akhmetzhanova and G.M. Bakan. Solution of a programming problem with inexactly specified initial data. Sov. J. Autom. Inf. Sci. 21, No.2, 55-58 translation from Avtomatika 1988, No.2, 54-56 (1988)., 1988. [34] Hisham Al-Mharmah and James M. Calvin. Optimal random non-adaptive algorithm for global optimization of Brownian motion. J. Global Optim., 8(1):81–90, 1996. [35] Hisham A. Al-Mharmah and James M. Calvin. Comparison of one-dimensional composite and non-composite passive algorithms. J. Global Optim., 15(2):169–180, 1999. [36] Aureli Alabert i Romero. On the optimization of hydroelectric power generation with random water inflows. Questii¨ o´, 15(3):307–348, 1991. [37] Chris M. Alaouze and Peter J. Lloyd. A generalization of Gurland’s theorem, with applications to economic behavior under uncertainty. Am. Stat. 40, 70-71, 1986. [38] Horst Albach. Capital budgeting and risk management. In Quant. Wirtsch.-Forsch., W. Krelle zum 60. Geb., 7-24, 1977. [39] Maria Albareda-Sambola and Elena Fernandez.´ The stochastic generalised assignment problem with Bernoulli demands. Top, 8(2):165–190, 2000. [40] Maria Albareda-Sambola, Maarten H. van der Vlerk, and Elena Fernandez.´ Exact solutions to a class of stochastic generalized assignment problems. European J. Oper. Res., 173(2):465–487, 2006. [41] Ya. Alber. Dynamical processes of stochastic approximation. Funct. Differ. Equ., 4(3-4):239–256 (1998), 1997. [42] Ya. I. Al’ber and S.V.Shil’man. Stochastic programming methods: convergence and nonasymptotic estimation of the convergence rate. In Stochastic optimization (Kiev, 1984), volume 81 of Lecture Notes in Control and Inform. Sci., pages 249–257. Springer, Berlin, 1986.

3 [43] Susanne Albers, Rolf H. Mohring,¨ Georg Ch. Pflug, and Rudiger¨ Schultz. 05031 Summary – Al- gorithms for Optimization with Incomplete Information. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [44] V. Albornoz, J. Arrate, and L. Contesse. Solucion de modelos de dimensionamiento de lotes no capacitados bajo incertidumbre en las demandas. Revista del Instituto Chileno de Investigacion Operativa, 6(1-2):52–62, 2001. [45] V. Albornoz and C. Canales. Planificacion de la conservacion y explotacion del langostino colorado usando un modelo de optimizacion estoc stica no-lineal con recurso. Informacion Tecnologica, 13(4):??, 2002. [46] V. Albornoz and L. Contesse. Modelos de optimizacion robusta para un problema de planificacion agregada de la produccion bajo incertidumbre en las demandas. Investigacion Operativa, 7(3):1– 16, 1999. [47] A. Albrecht, S.K. Cheung, K.C. Hui, K.S. Leung, and C.K. Wong. Optimal placements of flexible objects. I. Analytical results for the unbounded case. IEEE Trans. Comput., 46(8):890–904, 1997. [48] A. Albrecht, S.K. Cheung, K.C. Hui, K.S. Leung, and C.K. Wong. Optimal placements of flexible objects. II. A simulated annealing approach for the bounded case. IEEE Trans. Comput., 46(8):905– 929, 1997. [49] S.Christian Albright. A Markov-decision-chain approach to a stochastic assignment problem. Op- erations Res. 22, 61-64, 1974. [50] Michael Albritton, Alexander Shapiro, and Mark Spearman. Finite capacity production planning with random demand and limited information. Stochastic Programming E-Print Series, http: //www.speps.org, 2000. [51] David Aldous. Minimization algorithms and random walk on the d-cube. Ann. Probab., 11(2):403– 413, 1983. [52] I.A. Aleksandrov, V.P. Bulatov, S.B. Ognivtsev, and F.I. Yereshko. Solution of a stochastic programming problem concerning the distribution of water resources. In Stochastic optimization (Kiev, 1984), volume 81 of Lecture Notes in Control and Inform. Sci., pages 258–264. Springer, Berlin, 1986. [53] V.M. Aleksandrov, V.I. Sysoev, and V.V. Semeneva. Stochastische Optimierung von Systemen. Izv. Akad. Nauk SSSR, Tekh. Kibern. 1968, No. 5, 14-19, 1968. [54] A. Alessandri and T. Parisini. Nonlinear modelling of complex large-scale plants using neural networks and stochastic approximation. IEEE Transactions on Systems, Man, and Cybernetics – A, 27:750–757, 1997. [55] David L. J. Alexander, David Bulger, James M. Calvin, H. Edwin Romeijn, and Ryan L. Sherriff. Approximate implementations of pure random search in the presence of noise. J. Global Optim., 31(4):601–612, 2005. [56] M. Montaz Ali, Charoenchai Khompatraporn, and Zelda B. Zabinsky. A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems. J. Global Optim., 31(4):635–672, 2005. [57] M.M. Ali and C. Storey. Topographical multilevel single linkage. J. Global Optim., 5(4):349–358, 1994. [58] M.M. Ali, A. Torn,¨ and S. Viitanen. A numerical comparison of some modified controlled random search algorithms. J. Global Optim., 11(4):377–385, 1997.

4 [59] Montaz M. Ali. A probabilistic hybrid differential evolution algorithm. In Models and algorithms for global optimization, volume 4 of Springer Optim. Appl., pages 173–184. Springer, New York, 2007. [60] F.M. Allen, R.N. Braswell, and P.V. Rao. Distribution-free approximations for chance constraints. Operations Res., 22(3):610–621, 1974. [61] Sira Allende and Carlos Bouza. Stochastic programming approaches to the estimation of the mean in stratified population. Investigacion´ Oper., 14(2-3):109–118, 1993. Workshop on Stochastic Optimization: the State of the Art (Havana, 1992). [62] Sira Allende and Carlos Bouza. Random demands: optimum lot size and the newsboy problem. Investigacion´ Oper., 23(3):124–129, 2002. [63] A. Alonso-Ayuso, L. F. Escudero, C. Pizarro, H. E. Romeijn, and D. Romero Morales. On solving the multi-period single-sourcing problem under uncertainty. Comput. Manag. Sci., 3(1):29–53, 2006. [64] Mahmoud H. Alrefaei. Stochastic optimization using the standard clock simulation. Int. J. Appl. Math., 8(3):317–333, 2002. [65] Mahmoud H. Alrefaei and Ameen J. Alawneh. Solution quality of random search methods for discrete stochastic optimization. Math. Comput. Simulation, 68(2):115–125, 2005. [66] Mahmoud H. Alrefaei and Mohammad Almomani. Subset selection of best simulated systems. J. Franklin Inst., 344(5):495–506, 2007. [67] Mahmoud H. Alrefaei and Sigrun´ Andradottir.´ A simulated annealing algorithm with constant temperature for discrete stochastic optimization. Management Science, 45:748–764, 1999. [68] Mahmoud H. Alrefaei and Sigrun´ Andradottir.´ A modification of the stochastic ruler method for discrete stochastic optimization. European J. Oper. Res., 133(1):160–182, 2001. [69] Mahmoud H. Alrefaei and Sigrun´ Andradottir.´ Discrete stochastic optimization using variants of the stochastic ruler method. Naval Res. Logist., 52(4):344–360, 2005. [70] M.H. Alrefaei and S. Andradottir.´ A new search algorithm for discrete stochastic optimization. Proceedings of the 1995 Winter Simulation Conference 236–241, 1995. [71] M.H. Alrefaei and S. Andradottir.´ Discrete stochastic optimization via a modification of the stochastic ruler method. Proceedings of the 1996 Winter Simulation Conference 406–411, 1996. [72] A.Z. Al’terman. On a realization of random search for the construction of a separating metric. Probl. Sluchajnogo Poiska 7, 307-313, 1978. [73] A. Altman, M. Amann, G. Klaassen, A. Ruszczynski,´ and W. Schopp.¨ Cost-effective sulphur emission under uncertainty. European Journal of Operational Research, 90:395–412, 1996. [74] Adel A. Aly and John A. White. Probabilistic formulations of the multifacility Weber problem. Naval Res. Logist. Quart., 25(3):531–547, 1978. [75] Yakov Amihud. The effect of uncertainty in input quantities on the optimal expected input combi- nation. Manage. Sci. 23, 957-962, 1977. [76] H. M. Amman and D. A. Kendrick. Stochastic policy design in a learning environment with rational expectations. J. Optim. Theory Appl., 105(3):509–520, 2000. Special Issue in honor of Professor David G. Luenberger. [77] Hans M. Amman, David A. Kendrick, and Sudhakar Achath. Solving stochastic optimization models with learning and rational expectations. Econom. Lett., 48(1):9–13, 1995.

5 [78] G. Anandalingam. A stochastic programming process model for investment planning. Comput. Oper. Res. 14, 521-536, 1987. [79] Yu. G. Anastasyan, V.I. Gershovich, B.A. Yaroshevich, E.` I. Nenakhov, O.T. Burlak, M.B. Shchep- akin, and G.G. Murauskas. O nekotorykh algoritmakh negladkoi optimizatsii i diskretnogo programmirovaniya, volume 6 of Preprint 81. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1981. [80] E. J. Anderson and A. B. Philpott. On supply function bidding in electricity markets. In C. Green- gard and A. Ruszczynski,´ editors, Decision Making under Uncertainty: Energy and Power, volume 128 of IMA volumes on Mathematics and its Applications, pages 115–134. Springer-Verlag, 2002. [81] S. Andradottir.´ A method for discrete stochastic optimization. Management Science 1946–1961, 1995. [82] S. Andradottir.´ A stochastic approximation algorithm with varying bounds. Operations Research 1037–1048, 1995. [83] S. Andradottir.´ A global search method for discrete stochastic optimization. SIAM Journal on Optimization 513–530, 1996. [84] S. Andradottir.´ Optimization of the transient and steady-state behavior of discrete event systems. Management Science 717–737, 1996. [85] S. Andradottir.´ A scaled stochastic approximation algorithm. Management Science 475–498, 1996. [86] S. Andradottir.´ Simulation optimization. Handbook on Simulation (edited by Jerry Banks), Chapter 9, John Wiley and Sons New York, to appear. [87] Mikhail Andramonov, Jerzy Filar, Panos Pardalos, and Alexander Rubinov. Hamiltonian cycle problem via Markov chains and min-type approaches. In Approximation and complexity in numerical optimization (Gainesville, FL, 1999), pages 31–47. Kluwer Acad. Publ., Dordrecht, 2000. [88] G. Andreatta. Shortest path models in stochastic networks. In G. Andreatta, F. Mason, and P. Ser- afini, editors, Stochastics in Combinatorial Optimization, pages 178–186, Singapore, 1987. CISM, Udine, World Scientific Publishing Co. Pte. Ltd. [89] G. Andreatta and F. Mason. k-Eccentricity and absolute k-centrum of a probabilistic tree. Eur. J. Oper. Res. 19, 114-117, 1985. [90] G. Andreatta and G. Romanin-Jacur. Aircraft flow management under congestion. Transportation Science, 21(4):249–253, 1987. [91] G.B. Andreatta, G. Salinetti, and R.J.-B. Wets, editors. Stochastic programming. Baltzer Science Publishers BV, Amsterdam, 1995. Papers from the Sixth International Conference held in Udine, September 14–18, 1992, Ann. Oper. Res. 56 (1995). [92] Giovanni Andreatta and Luciano Romeo. Stochastic shortest paths with recourse. Networks 18, No.3, 193-204, 1988. [93] Giovanni Andreatta and Wolfgang J. Runggaldier. An approximation scheme for stochastic dynamic optimization problems. Math. Programming Stud., 27:118–132, 1986. Stochastic programming 84. I. [94] Colette Andrieu. Sur les solutions fiables d’un probleme` stochastique d’optimisation sous con- trainte. Rev. Roumaine Math. Pures Appl., 25(5):677–694, 1980. [95] Colette Andrieu. Sur certaines solutions fiables d’un probleme` stochastique de recherche optimale. Math. Operationsforsch. Statist. Ser. Optim., 12(1):115–122, 1981.

6 [96] Y.P. Aneja and K.P.K. Nair. Maximal expected flow in a network subject to arc failures. Networks 10, 45-57, 1980. [97] R. Anghelescu and V. Anghelescu. Recherches sur la programmation lineaire stochastique a recours. (Research on linear stochastic programming with recourse). In Proc. Symp. Math. Appl., Timisoara/Rom. 1985, 163-165, 1986. [98] R. Anghelescu and V. Anghelescu. etude´ sur la programmation lineaire´ stochastique. In Pro- ceedings of the Second Symposium of Mathematics and its Applications (Timis¸oara, 1987), pages 217–220, Timis¸oara, 1988. Res. Centre Acad. SR Romania. [99] R. Anghelescu and V. Anghelescu. Modalites´ d’approche des problemes` stochastiques d’optimum vectoriel. I. In Proceedings of the Third Symposium of Mathematics and its Applications (Timis¸oara, 1989), pages 123–128, Timis¸oara, 1990. Rom. Acad. [100] R. Anghelescu and V. Anghelescu. Solution optimale dans la programmation stochastique vecto- rielle. I. In Proceedings of the Fourth Symposium of Mathematics and its Applications (Timis¸oara, 1991), pages 16–21, Timis¸oara, 1992. Mirton. [101] Rodica Anghelescu and V. Anghelescu. Methods in determinating the optimal solution in problems of linear stochastic programming. Bul. S¸tiint¸. Tehn. Univ. Tehn. Timis¸oara Mat. Fiz., 38(52):94– 101, 1993. [102] Z.P. Anisimova and O.R. Petrenko. Limit theorems of stochastic optimization procedures in Markov random environments. In Stochastic systems and their applications (Russian), pages 4–8. Akad. Nauk Ukrain. SSR Inst. Mat., Kiev, 1990. [103] A.N. Antamoshkin and M.A. Valishevskij. Complete effectivity investigation of methods optimizing functionals with Boolean derivatives taking random search as example. In Applications of random search to the solution of applied problems, Collect. sci. Works, Kemerovo 1982, 48-54, 1982. [104] K.A. Antanavichyus and S.S. Chirba. A stochastic programming problem for preparing rational production programs for branch complexes. Ehkon. Mat. Metody 21, 1048-1057, 1985. [105] K.A. Antanavichyus and S.S. Chirba. A problem of stochastic programming for preparation of rational production programs for branch complexes. Ekonom.` i Mat. Metody, 21(6):1048–1057, 1985. [106] P.L. Antonelli and J.M. Skowronski. Adaptive identification of environmental stress for the management of plant growth. Math. Comput. Modelling 10, No.1, 27-35, 1988. [107] G.E. Antonov and V. Ja. Katkovnik. A generalization of the concept of statistical gradient. Avtomat. i Vycisl.ˇ Tehn. (Riga), 4:25–30, 1972. [108] I.L. Antonov. A steady-state process in a two-dimensional extremal system in the presence of pro- hibited regions and a random method of search. Vestnik Moskov. Univ. Ser. I Mat. Meh., 25(5):117– 122, 1970. [109] I.L. Antonov. A transition process in a two-dimensional extremal system in the presence of for- bidden domains, in a random method of search. In Problems of statistical optimization (Russian), pages 69–80. Izdat. “Zinatne”, Riga, 1971. [110] Bruno Apolloni and Ferdinando Pezzella. Confidence intervals in the solution of stochastic integer linear programming problems. In Stochastics and optimization, Sel. Pap. ISSO Meet., Gorguano/Italy 1982, Ann. Oper. Res. 1, 67-78, 1984. [111] N.I. Arbuzova. Ueber die stochastische :-Stabilitaet der Loesung einer Aufgabe der quadratischen Programmierung. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1967, Nr. 3, 35-40, 1967.

7 [112] N.I. Arbuzova. Interdependence of the stochastic -stabilities of linear and linear fractional programming problems of a special form. Ekonom.` i Mat. Metody, 4:108–110, 1968. [113] N.I. Arbuzova and V.L. Danilov. Zur Erweiterung des Begriffs der Stabilitaet des Problems der linearen Programmierung. Kibernetika, Kiev 1970, No.4, 139-140, 1970. [114] F. Archetti. Evaluation of random gradient techniques for unconstrained optimization. Calcolo 12, 83-94, 1975. [115] F. Archetti, G. Di Pillo, and M. Lucertini, editors. Stochastic programming, volume 76 of Lec- ture Notes in Control and Information Sciences, Berlin, 1986. Springer-Verlag. Papers from the conference held in Gargnano, September 15–21, 1983. [116] F. Archetti and F. Frontini. The application of a global optimization method to some technological problems. In Towards global optimisation 2, Work shops Varenna 1976 and Bergamo 1977, 179- 188, 1978. [117] F. Archetti, A. Gaivoronski, and A. Sciomachen. Sensitivity analysis and optimization of stochastic Petri nets. Discrete Event Dyn. Syst. 3, No.1, 5-37, 1993. [118] F. Archetti and F. Schoen. A survey on the global optimization problem: General theory and computational approaches. In Stochastics and optimization, Sel. Pap. ISSO Meet., Gorguano/Italy 1982, Ann. Oper. Res. 1, 87-110, 1984. [119] Francesco Archetti. Analysis of stochastic strategies for the numerical solution of the global optimization problem. In Numerical techniques for stochastic systems, Conf., Gargnano/Italy 1979, 275-295, 1980. [120] Francesco Archetti. A probabilistic algorithm for global optimization problems with a dimension- ality reduction technique. In Optimization techniques (Proc. Ninth IFIP Conf., Warsaw, 1979), Part 2, volume 23 of Lecture Notes in Control and Information Sci., pages 36–42, Berlin, 1980. Springer. [121] Francesco Archetti and Bruno Betro.` Stochastic models and optimization. Boll. Un. Mat. Ital. A (5), 17(2):295–301, 1980. [122] T. W. Archibald, C. S. Buchanan, K. I. M. McKinnon, and L. C. Thomas. Nested Benders decomposition and dynamic programming for reservoir optimisation. Journal of the Operational Research Society, 50(5):468–479, 1999. [123] T. W. Archibald, C. S. Buchanan, L. C. Thomas, and K. I. M. McKinnon. Controlling multireservoir systems. European Journal of Operational Research, 129(3):619–626, 2001. [124] R. Ardanuy and A. Alcala.´ Weak inﬁnitesimal operators and stochastic differential games. Stochas- tica, 13(1):5–12, 1992. [125] K. A. Ariyawansa, C. Cacho, and A. J. Felt. A family of stochastic programming test problems based on a model for tactical manpower planning. J. Math. Model. Algorithms, 4(4):369–390, 2005. [126] K. A. Ariyawansa and Andrew J. Felt. On a new collection of stochastic linear programming test problems. INFORMS J. Comput., 16(3):291–299, 2004. [127] K. A. Ariyawansa and Yuntao Zhu. Stochastic semideﬁnite programming: a new paradigm for stochastic optimization. 4OR, 4(3):239–253, 2006. [128] K. A. Ariyawansa and Yuntao Zhu. A class of volumetric barrier decomposition algorithms for stochastic quadratic programming. Appl. Math. Comput., 186(2):1683–1693, 2007.

8 [129] K.A. Ariyawansa. Performance of a benchmark implementation of the Van Slyke and Wets algorithm for stochastic programs on the alliant FX/8. In Dongarra, Jack (ed.) et al., Proceedings of the ﬁfth SIAM conference on parallel processing for scientiﬁc computing, held in Houston, TX, USA, March 25-27, 1991. Philadelphia, PA: SIAM, (ISBN 0-89871-303-X/pbk). 186- 192, 1992. [130] Vadim I. Arkin. Stochastic optimization approach to dynamic problems with jump changing structure. In Stochastic programming methods and technical applications (Neubiberg/Munich, 1996), pages 104–110. Springer, Berlin, 1998. [131] V.I. Arkin. Economic dynamics and discretely varying technology. Probabilistic approach. In Probability and mathematical economics, Moskva, 3-30, 1988. [132] V.I. Arkin and I.V. Evstigneev. Probabilistic models of control and economic dynamics. (Veroyat- nostnye modeli upravleniya i ehkonomicheskoj dinamiki). Moskva: ”Nauka”., 1979. [133] V.I. Arkin, A. Shiraev, and R. Wets, editors. Stochastic Optimization. Proceedings of the Interna- tional Conference, Kiev 1984. Springer, Berlin, 1986. LN in Control and Information Sciences 81. [134] V.I. Arkin and S.A. Smolyak. On the structure of optimality criteria in stochastic optimization models. In Stochastic optimization, Proc. Int. Conf., Kiev/USSR 1984, Lect. Notes Control Inf. Sci. 81, 275-286, 1986. [135] Ronald D. Armstrong and Joseph L. Balintfy. A chance constrained multiple choice programming algorithm with applications. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 301–325. Academic Press, London, 1980. [136] Klaus-Peter Arnold. Stochastische Transportprobleme. Verlag Dr. Kovac,ˇ Hamburg, 1987. [137] H. Arsham. Performance extrapolation in discrete-event systems simulation. International Journal of Systems Science, 27(9):863–869, 1996. [138] H. Arsham. Stochastic optimization of discrete event systems simulation. International Journal of Microelectronics and Reliability, 36(10):1357–1368, 1996. [139] H. Arsham. Goal seeking problem in discrete event systems simulation. International Journal of Microelectronics and Reliability, 37(3):391–395, 1997. [140] H. Arsham. Algorithms for sensitivity information in discrete-event systems simulation. Simulation Practice and Theory, 6(1):1–22, 1998. [141] H. Arsham. Techniques for Monte Carlo optimizing. Monte Carlo Methods Appl., 4(3):181–229, 1998. [142] Zvi Artstein. Convergence rates for the optimal values of allocation processes. Math. Oper. Res. 9, 348-355, 1984. [143] Zvi Artstein. Limit laws for multifunctions applied to an optimization problem. In Multifunctions and integrands (Catania, 1983), volume 1091 of Lecture Notes in Math., pages 66–79. Springer, Berlin, 1984. [144] Zvi Artstein. Probing for information in two-stage stochastic programming and the associated consistency. In Asymptotic statistics (Prague, 1993), Contrib. Statist., pages 21–33. Physica, Hei- delberg, 1994. [145] Zvi Artstein. Sensitivity with respect to the underlying information in stochastic programs. J. Com- put. Appl. Math., 56(1-2):127–136, 1994. Stochastic programming: stability, numerical methods and applications (Gosen, 1992).

9 [146] Zvi Artstein. Gains and costs of information in stochastic programming. Ann. Oper. Res., 85:129– 152, 1999. Stochastic programming. State of the art, 1998 (Vancouver, BC). [147] Zvi Artstein and Roger J.-B. Wets. Approximating the integral of a multifunction. J. Multivariate Anal., 24(2):285–308, 1988. [148] Zvi Artstein and Roger J.-B. Wets. Sensors and information in optimization under stochastic uncertainty. Math. Oper. Res., 18(3):523–547, 1993. [149] Zvi Artstein and Roger J.-B. Wets. Stability results for stochastic programs and sensors, allowing for discontinuous objective functions. SIAM J. Optim., 4(3):537–550, 1994. [150] Zvi Artstein and Roger J.-B. Wets. Consistency of minimizers and the SLLN for stochastic programs. J. Convex Anal., 2(1-2):1–17, 1995. [151] Enrique R. Arzac. Profits and safety in the theory of the firm under price uncertainty. Internat. econom. Review 17, 163-171, 1976. [152] R.W. Ashford and E.M.L. Beale. A cross-estimation technique for using control variables in stochastic simulations. European J. Oper. Res., 40(3):352–362, 1989. [153] Soeren Asmussen and Reuven Rubinstein. Performance evaluation for the score function method in sensitivity analysis and stochastic optimization. In Simulation and optimization, Proc. Int. Work- shop Comput. Intensive Methods Simulation Optimization, Laxenburg/Austria 1990, Lect. Notes Econ. Math. Syst. 374, 1-13, 1992. [154] P.G. Asojanc. A problem of Robbins. Kibernetika (Kiev), 2:105–106, 1976. [155] A. S. Asratyan and N. N. Kuzyurin. Approximation of optima of integer programs of covering- packing type. Diskret. Mat., 12(1):96–106, 2000. [156] N.V. Astanovskaya, V.I. Varshavskij, V.P. Grigorenko, and V.M. Revako. Adaptive algorithms for the decentralized distribution of resources under conditions of uncertainty. Probl. Sluchajnogo Poiska 7, 296-303, 1978. [157] H. Attouch. Variational averaging of problems with stochastic data. In Inverse methods in action, Proc. Multicent. Meet., Montpellier/Fr. 1989, 396-404, 1990. [158] H. Attouch and R.J-B. Wets. Quantitative stability of variational systems i: the epigraphical distance. Transactions of the American Mathematical Society, 328:695–729, 1991. [159] Kelly T. Au, Julia L. Higle, and Suvrajeet Sen. Inexact subgradient methods with applications in stochastic programming. Math. Programming, 63(1, Ser. A):65–82, 1994. [160] I.L. Averbakh. An algorithm for solving an m-dimensional knapsack problem with random coefficients. Diskret. Mat., 2(3):3–9, 1990. [161] I.L. Averbakh. An additive method for optimization of two-stage stochastic systems with discrete variables. Sov. J. Comput. Syst. Sci. 28, No.4, 161-165 translation from Izv. Akad. Nauk SSSR, Tekh. Kibern. 1990, No.1, 162-166 (1990)., 1990. [162] I.L. Averbakh. An iterative decomposition method in one-stage problems of stochastic integer programming. Zh. Vychisl. Mat. i Mat. Fiz., 30(10):1467–1476, 1990. [163] I.L. Averbakh. An iterative method of solving two-stage discrete stochastic programming problems with additively separable variables. Comput. Math. Math. Phys. 31, No.6, 21-27 translation from Zh. Vychisl. Mat. Mat. Fiz. 31, No.6, 810-818 (1991)., 1991. [164] David Avis. On the extreme rays of the metric cone. Canad. J. Math., 32(1):126–144, 1980.

10 [165] M. Avriel and D.J. Wilde. Stochastic geometric programming. In Proceedings of the Princeton Symposium on Mathematical Programming (Princeton Univ., 1967), pages 73–91, Princeton, N.J., 1970. Princeton Univ. Press. [166] M. Avriel and A.C. Williams. The value of information and stochastic programming. Oper. Res. 18, 947-954, 1970. [167] S.V. Avrutik and N.P. Dekanova. Two approaches in nonlinear and stochastic programming. In Numerical methods in analysis (applied mathematics) (Russian), pages 5–11. Akad. Nauk SSSR Sibirsk. Otdel. Sibirsk. Energet.` Inst., Irkutsk, 1976. [168] S.V. Avrutin. On the formulation and solution of some non-linear stochastic problems. In Opti- mization methods and their applications, 9, Work Collect., Irkutsk 1979, 5-13, 1979. [169] Shimon Awerbuch, Joseph G. Ecker, and William A. Wallace. A note: Hidden nonlinearities in the application of goal programming. Management Sci. 22, 918-920, 1976. [170] Abbas N. Azad and Naveed Saleem. A chance constrained approach to bank balance sheet management: A simple model with a computational example. J. Inf. Optimization Sci. 12, No.3, 363-386, 1991. [171] F. Azadivar and J. Talavage. Optimization of stochastic simulation models. Math. Comput. Simu- lation 22, 231-241, 1980. [172] Farhad Azadivar and Young-Hae Lee. Optimization of discrete variable stochastic systems by computer simulation. Math. Comput. Simulation 30, No.4, 331-345, 1988. [173] Yossi Azar and Yossi Richter. An improved algorithm for CIOQ switches. In S. Albers, R.H. Mohring,¨ G.Ch. Pﬂug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimiza- tion with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [174] N. Baba. Global optimization of functions by the random optimization method. Int. J. Control 30, 1061-1065, 1979. [175] N. Baba. Convergence of a random optimization method for constrained optimization problems. J. Optimization Theory Appl. 33, 451-461, 1981. [176] N. Baba. A hybrid algorithm for ﬁnding a global minimum. Int. J. Control 37, 929-942, 1983. [177] Norio Baba and Akira Morimoto. Three approaches for solving the stochastic multiobjective programming problem. In Stochastic optimization. Numerical methods and technical applications, Proc. GAMM/IFIP-Workshop, Neubiberg/Ger. 1990, Lect. Notes Econ. Math. Syst. 379, 93-109, 1992. [178] Norio Baba and Akira Morimoto. Stochastic approximation method for solving the stochastic multiobjective programming problem. Internat. J. Systems Sci., 24(4):789–796, 1993. [179] A.S. Babanin. A generalization of the arctangent law. Teor. Veroyatnost. i Mat. Statist., 28:3–5, 1983. [180] Leonard´ Bacaud, Claude Lemarechal,´ Arnaud Renaud, and Claudia Sagastizabal.´ Bundle methods in stochastic optimal power management: a disaggregated approach using preconditioners. Com- put. Optim. Appl., 20(3):227–244, 2001. [181] Thomas Back.¨ Evolutionary algorithms in theory and practice. The Clarendon Press Oxford University Press, New York, 1996. Evolution strategies, evolutionary programming, genetic algorithms. [182] Anna Badach. An application of reliability theory to stochastic linear programming problems. Przeglk ad Statyst., 22(4):569–584, 1975.

11 [183] A.M. Bagdasarov and G.A. Samatov. Ein Modell der Perspektivplanung der Arbeit eines Trans- portsystems. Dokl. Akad. Nauk UzSSR 1978, No.11, 15-17, 1978. [184] Adib Bagh and Michael Casey. An ergodic theorem for random lagrangians with an application to stochastic programming. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [185] Adib Bagh and Michael S. Casey. An ergodic theorem for random Lagrangians with an application to stochastic programming. Int. J. Pure Appl. Math., 14(3):343–363, 2004. [186] O. Bahn, O. Du Merle, J.-L. Gofﬁn, and J.-P. Vial. A cutting plane method from analytic centers for stochastic programming. Math. Programming, 69(1, Ser. B):45–73, 1995. Nondifferentiable and large-scale optimization (Geneva, 1992). [187] D. Bai, T.J. Carpenter, and J.M. Mulvey. Making a case for robust models. Management Science, 43:895–907, 1997. [188] Matthew D. Bailey, Steven M. Shechter, and Andrew J. Schaefer. SPAR: stochastic programming with adversarial recourse. Oper. Res. Lett., 34(3):307–315, 2006. [189] Michael P. Bailey. Solving a class of stochastic minimization problems. Oper. Res. 42, No.3, 428-438, 1994. [190] T.G. Bailey, P. Jensen, and D.P. Morton. Response surface analysis of two-stage stochastic linear programming with recourse. Naval Research Logistics, 46:753–778, 1999. [191] M.M. Bajzel’ and G.S. Tarasenko. The investigation of an adaptive optimization algorithm in the situation of noise. Probl. Sluchajnogo Poiska 9, 106-124, 1981. [192] V. Balachandran. Generalized transportation networks with stochastic demands: an operator- theoretic approach. Networks, 9(2):169–184, 1979. [193] A.V. Balakrishnan. Stochastic optimization theory in Hilbert spaces. I. Appl. Math. Optimization 1, 97-120, 1974. [194] Egon Balas. Nonconvex quadratic programming via generalized polars. SIAM J. Appl. Math., 28:335–349, 1975. [195] E.J. Balder. An extension of the usual model in statistical decision theory with applications to stochastic optimization problems. J. Multivariate Anal., 10(3):385–397, 1980. [196] Erik J. Balder. Existence without explicit compactness in stochastic dynamic programming. Math. Oper. Res., 17(3):572–580, 1992. [197] J.F. Balducchi, G. Cohen, J.-C. Dodu, M. Goursat, Herz, J.-P. Quadrat, and M. Viot. Three methods for optimizing the capacities of an electrical transmission network. 8th IFAC World Congress, Kyoto, Japan, 1981. [198] J.L. Balintfy. Nonlinear programming for models with joint chance constraints. In Integer nonlin. Program., 337-352, 1970. [199] Joseph L. Balintfy. Applications of mathematical programming to optimize human diets. In Symp. Math. 19, Program. mat. Appl., Convegno 1974, 313-339, 1976. [200] Michael O. Ball, Robert Hoffman, Amedeo R. Odoni, and Ryan Rifkin. A stochastic integer program with dual network structure and its application to the ground-holding problem. Oper. Res., 51(1):167–171, 2003. [201] Enrique Ballestero. Stochastic goal programming: a mean-variance approach. European J. Oper. Res., 131(3):476–481, 2001.

12 [202] Enrique Ballestero. Stochastic linear programming with scarce information: an approach from expected utility and bounded rationality applied to the textile industry. Eng. Optim., 38(4):425– 440, 2006. [203] Simonetta Balsamo, Vittoria de Nitto Persone,´ and Raif Onvural. Analysis of queueing networks with blocking. Kluwer Academic Publishers, Boston, MA, 2001. [204] Shumeet Baluja. Using a priori knowledge to create probabilistic models for optimization. Inter- nat. J. Approx. Reason., 31(3):193–220, 2002. Synergies between evolutionary computation and probabilistic graphical models. [205] A.K. Balyko. A problem of stochastic programming. Engrg. Cybernetics, 20(1):43–49 (1983), 1982. [206] Julio R. Banga and Warren D. Seider. Global optimization of chemical processes using stochastic algorithms. In State of the art in global optimization (Princeton, NJ, 1995), volume 7 of Nonconvex Optim. Appl., pages 563–583. Kluwer Acad. Publ., Dordrecht, 1996. [207] Peter Bank and Frank Riedel. Optimal consumption choice with intertemporal substitution. Ann. Appl. Probab., 11(3):750–788, 2001. [208] G. Bao and C.G. Cassandras. Stochastic comparison algorithm for continuous optimization with estimation. J. Optim. Theory Appl., 91(3):585–615, 1996. [209] A.P. Baranov. Convergence of a class of stochastic approximation procedures. Kibernetika (Kiev), 4:64–69, 135, 1987. [210] V.V. Baranov. A dynamic programming algorithm in stochastic systems. U.S.S.R. Comput. Math. Math. Phys. 18, No.6, 55-68 translation from Zurn. vycislit. Mat. mat. Fiz. 18, No.6, 1416-1429 (1978)., 1979. [211] V.V. Baranov. Optimal dynamic pattern recognition and decision making. Zh. Vychisl. Mat. i Mat. Fiz., 34(7):984–1000, 1994. [212] V.V. Baranov and N.V. Tret’yakova. The averaging sequence method in Markov decision processes with periodic strategies. Vestnik Khar’ kov. Gos. Univ., 286:34–50, ii, 1986. [213] J. F. Bard, D. P. Morton, and Y. Wang. Workforce planning at USPS mail processing distribution centers using stochastic optimization. Annals of Operations Research, 155:51–78, 2007. [214] Jacob Barhen, Vladimir Protopopescu, and David Reister. TRUST: a deterministic algorithm for global optimization. Science, 276(5315):1094–1097, 1997. [215] Bill Baritompa and Eligius M. T. Hendrix. On the investigation of stochastic global optimization algorithms. J. Global Optim., 31(4):567–578, 2005. [216] W. P. Baritompa, M. Dur,¨ E. M. T. Hendrix, L. Noakes, W. J. Pullan, and G. R. Wood. Matching stochastic algorithms to objective function landscapes. J. Global Optim., 31(4):579–598, 2005. [217] W.P. Baritompa, Zhang Baoping, R.H. Mladineo, G.R. Wood, and Z.B. Zabinsky. Towards pure adaptive search. J. Global Optim., 7(1):93–110, 1995. [218] David P. Baron. Information in two-stage programming under uncertainty. Naval Res. Logist. Quart., 18:169–176, 1971. [219] Diana Barro and Elio Canestrelli. A decomposition approach in multistage stochastic programming. Rend. Studi Econ. Quant., pages 73–88, 2005. [220] F.Hutton Barron and Kenneth D. Mackenzie. A constrained optimization model of risky decisions. J. math. Psychology 10, 60-72, 1973.

13 [221] Russell R. Barton. Minimization algorithms for functions with random noise. Amer. J. Math. Management Sci., 4(1-2):109–138, 1984. Statistics and optimization : the interface. [222] A.M. Bartsalkin and D.K. Zambitskij. On an allocation problem with probabilistic demands. Mat. Issled. 87, 10-15, 1986. [223] Kengy Barty, P. Carpentier, J.-P. Chancelier, G. Cohen, M. de Lara, and T. Guilbaud. Dual effect free stochastic controls. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [224] Kengy Barty, Jean-Sebastien Roy, and Cyrille Strugarek. A perturbed gradient algorithm in hilbert spaces. Optimization Online, http://www.optimization-online.org, 2005. [225] Kengy Barty, Jean-Sebastien Roy, and Cyrille Strugarek. A stochastic gradient type algorithm for closed loop problems. Stochastic Programming E-Print Series, http://www.speps.org, 2005. [226] A.I. Barvinok. Statistical sums in optimization and computational problems. Algebra i Analiz, 4(1):3–53, 1992. [227] Alexander Barvinok. Approximate counting via random optimization. Random Structures Algo- rithms, 11(2):187–198, 1997. [228] A.M. Barzalkin and D.K. Zambitskij. An algorithm for the solution of a stochastic allocation problem. Mat. Issled. 96, 3-7, 1987. [229] Tamer Bas¸ar. A general theory for Stackelberg games with partial state information. Large Scale Systems, 3(1):47–56, 1982. [230] John Basel, III and Thomas R. Willemain. Random tours in the traveling salesman problem: analysis and application. Comput. Optim. Appl., 20(2):211–217, 2001. [231] Cock Bastian and Alexander H.G. Rinnooy Kan. The stochastic vehicle routing problem revisited. Eur. J. Oper. Res. 56, No.3, 407-412, 1992. [232] Fabian Bastin. An adaptive trust-region approach for nonlinear stochastic optimisation with an application in discrete choice theory. In S. Albers, R.H. Mohring,¨ G.Ch. Pﬂug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [233] Fabian Bastin, Cinzia Cirillo, and Philippe L. Toint. Convergence theory for nonconvex stochastic programming with an application to mixed logit. Math. Program., 108(2-3, Ser. B):207–234, 2006. [234] Vic Baston and Anatole Beck. Generalizations in the linear search problem. Israel J. Math., 90(1- 3):301–323, 1995. [235] Dipak R. Basu and Alexis Lazaridis. Evaluation of intersectoral investment allocation in India, 1951-1970. An application of stochastic optimal control by pseudo-inverse. Int. J. Syst. Sci. 11, 889-906, 1980. [236] Vladimir Batagelj. Notes on the dynamic clusters method. In IV conference on applied mathematics (Split, 1984), pages 139–146. Univ. Split, Split, 1985. [237] John Bather. Randomised allocation of treatments in sequential trials. Adv. Appl. Probab. 12, 174-181, 1980. [238] V.D. Batukhtin and L.N. Korotaeva. A stochastic method for searching of an extremum of discontinuous functions. In Nonsmooth problems of optimization and control (Russian), pages 4–11, 111, Sverdlovsk, 1988. Akad. Nauk SSSR Ural. Otdel.

14 [239] V.D. Batukhtin and L.A. Maiboroda. Optimization of Discontinuous Functions. Nauka, Moscow, 1984. (in Russian). [240] V.D. Batukhtin and L.A. Majboroda. On a formalization of extremal problems. Sov. Math., Dokl. 21, 1-5 translation from Dokl. Akad. Nauk SSSR 250, 11-14 (1980)., 1980. [241] Vijay S. Bawa. On chance constrained programming problems with joint constraints. Management Sci., 19:1326–1331, 1972/73. [242] V.S. Bawa. A simple concavity condition for a class of chance-constrained programming problems with joint constraints. Operations Res. 24, 378-380, 1976. [243] David S. Bayard. Proof of quasi-adaptivity for the m-measurement feedback class of stochastic control policies. IEEE Trans. Autom. Control AC-32, 447-451, 1987. [244] Guzin¨ Bayraksan and David P. Morton. Assessing solution quality in stochastic programs. Stochas- tic Programming E-Print Series, http://www.speps.org, 2005. [245] Guzin¨ Bayraksan and David P. Morton. Assessing solution quality in stochastic programs. Math. Program., 108(2-3, Ser. B):495–514, 2006. [246] M.S. Bazaraa, J.J. Goode, and M.Z. Nashed. On the cones of tangents with applications to mathematical programming. J. Optimization Theory Appl., 13:389–426, 1974. [247] L.G. Bazenovˇ and A.M. Gupal. A certain stochastic analogue of the method of feasible directions. Kibernetika (Kiev), 5:94–95, 1973. [248] Z.A. Bazhenova. Choice models for rational strategies to develop specialized and industrial capacities of the industrial base in case of indetermination. Issled. Oper. ASU 20, 36-44, 1982. [249] E.M.L. Beale. Some uses of mathemtical programming systems to solve problems that are not linear. Operational Res. Quart., 26(3, part 2):609–618, 1975. [250] E.M.L. Beale, G.B. Dantzig, and R.D. Watson. A first order approach to a class of multi-time- period stochastic programming problems. Math. Programming Stud., 27:103–117, 1986. Stochas- tic programming 84. I. [251] E.M.L. Beale, J.J.H. Forrest, and C.J. Taylor. Multi-time-period stochastic programming. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 387–402. Aca- demic Press, London, 1980. [252] Luca Becchetti, Stefano Leonardi, Alberto Marchetti-Spaccamela, Guidouca Schaefer, and Tjark Vredeveld. Average Case and Smoothed Competitive Analysis of the Multi-Level Feedback Al- gorithm. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl. de/05031, 2005. [253] A.A. Bedel’baev, A.B. Kopeikin, and Ju.S. Popkov. Efficiency of mixed strategies in optimization problems. Autom. Remote Control 3 1372-1377 (1977), translation from Avtom. Telemekh. 1976, No.9, 90-95 (1976)., 1976. [254] C.N. Beer and B.L. Foote. A procedure to rank bases by probability of being optimal using imbed- ded hyperspheres. Math. Programming, 9(1):123–128, 1975. [255] Zuzana Beerliova, Felix Eberhard, Thomas Erlebach, Alexander Hall, Michael Hoffmann, Matus Mihalak, and L. Shankar Ram. Network Discovery and Verification. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005.

15 [256] H. Beigy and M. R. Meybodi. Stochastic optimization using continuous action-set learning automata. Sci. Iran., 12(1):14–25, 2005. [257] I.¯ V. Beiko and P.N. Zin’ko. Some probability estimates for algorithms of stochastic programming with a constant step multiplier. Kibernetika (Kiev), 2:91–95, 1978. [258] V.Z.(ed.) Belen’kii and V.A.(ed.) Volkonskii. Iterative Methoden in der Theorie der Spiele und Pro- grammierung. (Iterativnye metody v teorii igr i programmirovanii.). Ekonomiko-matematiceskaja biblioteka. Moskau: Verlag ’Nauka’, Hauptredaktion fuer physikalisch-mathematische Literatur., 1974. [259] Claude Belisle,´ Arnon Boneh, and Richard J. Caron. Convergence properties of hit-and-run sam- plers. Comm. Statist. Stochastic Models, 14(4):767–800, 1998. [260] R. Bellman and M. Roosta. A stochastic travelling salesman problem. Stochastic Anal. Appl. 1, 159-161, 1983. [261] Ju. A. Belov.¯ A two-level stochastic programming problem. Dokl. Akad. Nauk Ukrain. SSR Ser. A, 5:371–375, 400, 1979. [262] Ju. A. Belov.¯ Block stochastic optimization problem with probabilistic constraints and deterministic solution. Dokl. Akad. Nauk Ukrain. SSR Ser. A, 8:63–66, 89, 1980. [263] Ju. A. Belov.¯ Monotonicity of a functional for an iterative algorithm for the block problem with random parameters. Zh. Vychisl. Mat. i Mat. Fiz., 20(2):298–305, 549, 1980. [264] Ju. A. Belov.¯ Two-level optimization for a single-step stochastic programming problem with probability constraints. Vychisl. Prikl. Mat. (Kiev), 43:78–85, 158, 1981. [265] Yu. A. Belov.¯ The block two-stage stochastic programming problem with continuous distribution of the constraint vector. Cybernetics, 16(1):145–148, 1980. [266] Yu. A. Belov.¯ Decomposition of two-stage problems of stochastic programming of block type. Dokl. Akad. Nauk SSSR, 255(4):811–813, 1980. [267] Yu. A. Belov. A stochastic normal model with solving distributions for block-type extremal problems. Cybernetics, 19(2):239–247, 1983. [268] Yu.A. Belov. Two-level problem of stochastic programming. Dopov. Akad. Nauk Ukr. RSR, Ser. A 1979, 370-374, 1979. [269] Yu.A. Belov. Monotonicity with respect to functional of an iterative algorithm for the block problem with random parameters. U.S.S.R. Comput. Math. Math. Phys. 20, No.2, 24-32 translation from Zh. Vychisl. Mat. Mat. Fiz. 20, 298-305 (1980)., 1980. [270] Yu.A. Belov. A single-stage block type stochastic problem with row probability constraints. U.S.S.R. Comput. Math. Math. Phys. 21, No.5, 58-64 translation from Zh. Vychisl. Mat. Mat. Fiz. 21, 1133-1139 (1981)., 1981. [271] Yu.A. Belov, A.I. Yastremskij, and D.V. Usovskij. Experimental design in the imitative modelling with the help of methods of stochastic programming. Vychisl. Prikl. Mat., Kiev 48, 133-139, 1982. [272] L.S. Belyaev. Some statements and ways of solving dynamic optimization problems under uncertainty. In Optim. Techn., IFIP techn. Conf. Novosibirsk 1974, Lect. Notes Comput. Sci. 27, 18-21, 1975. [273] L.S. Belyaev. The solution of complex optimization problems under uncertainty conditions. (Reshenie slozhnykh optimizatsionnykh zadach v usloviyakh neopredelennosti). Akademiya Nauk SSSR, Sibirskoe Otdelenie, Sibirskij Ehnergeticheskij Institut. Novosibirsk: Izdatel’stvo ”Nauka”, Sibirskoe Otdelenie., 1978.

16 [274] F. Ben Abdelaziz, P. Lang, and R. Nadeau. Pointwise efﬁciency in multiobjective stochastic linear programming. J. Oper. Res. Soc. 45, No.11, 1324-1334, 1994. [275] F. Ben Abdelaziz, P. Lang, and R. Nadeau. Distributional unanimity in multiobjective stochastic linear programming. In Multicriteria analysis (Coimbra, 1994), pages 225–236. Springer, Berlin, 1997. [276] F. Ben Abdelaziz, P. Lang, and R. Nadeau. Dominance and efﬁciency in multiobjective stochastic linear programming. In Advances in multiple objective and goal programming (Torremolinos, 1996), volume 455 of Lecture Notes in Econom. and Math. Systems, pages 160–169. Springer, Berlin, 1997. [277] F. Ben Abdelaziz and H. Masri. Stochastic programming with fuzzy linear partial information on probability distribution. European J. Oper. Res., 162(3):619–629, 2005. [278] Yakov Ben-Haim and Isaac Elishakoff. Convex models of uncertainty in applied mechanics. Studies in Applied Mechanics 25. Elsevier, Amsterdam, 1990. [279] Adi Ben-Israel and Aharon Ben-Tal. Duality and equilibrium prices in economics of uncertainty. Math. Methods Oper. Res., 46(1):51–85, 1997. [280] A. Ben-Tal and E. Hochman. More bounds on the expectation of a convex function of a random variable. J. Appl. Probability, 9:803–812, 1972. [281] A. Ben-Tal and M. Teboulle. Penalty functions and duality in stochastic programming via - divergence functionals. Math. Oper. Res., 12(2):224–240, 1987. [282] Aharon Ben-Tal. The entropic penalty approach to stochastic programming. Math. Oper. Res., 10(2):263–279, 1985. [283] Aharon Ben-Tal and Adi Ben-Israel. A recourse certainty equivalent for decisions under uncertainty. Ann. Oper. Res., 30(1-4):3–44, 1991. Stochastic programming, Part I (Ann Arbor, MI, 1989). [284] Aharon Ben-Tal and Eithan Hochman. Stochastic programs with incomplete information. Opera- tions Res., 24(2):336–347, 1976. [285] Aharon Ben-Tal, Tamar Margalit, and Arkadi Nemirovski. Robust modeling of multi-stage portfolio problems. In High performance optimization, pages 303–328. Kluwer Acad. Publ., Dordrecht, 2000. [286] Aharon Ben-Tal, Tamar Margalit, and Arkadi Nemirovski. Robust modeling of multi-stage portfolio problems. In High performance optimization, volume 33 of Appl. Optim., pages 303–328. Kluwer Acad. Publ., Dordrecht, 2000. [287] Aharon Ben-Tal and Marc Teboulle. The duality between expected utility and penalty in stochastic linear programming. In Stochastic programming (Gargnano, 1983), volume 76 of Lecture Notes in Control and Inform. Sci., pages 151–161. Springer, Berlin, 1986. [288] Aharon Ben-Tal and Marc Teboulle. Expected utility, penalty functions, and duality in stochastic nonlinear programming. Management Sci., 32(11):1445–1466, 1986. [289] Aharon Ben-Tal and Marc Teboulle. Portfolio theory for the recourse certainty equivalent maximizing investor. Ann. Oper. Res. 31, 479-499, 1991. [290] P. Benedek, A. Darazs, and J.D. Pinter. Risk management of accidental water pollution: An illustrative application. Water Science and Technology, 22:265–274, 1990. [291] Viktor Benes. Conservative expectation estimators by means of an optimization moment problem. Ekon.-Mat. Obz. 21, 407-417, 1985.

17 [292] A. Benveniste, P. Bernhard, and G. Cohen. On the decomposition of stochastic control problems. 1rst IFAC Symposium on Large Scale Systems Theory and Applications, Udine, Italie, 1976. [293] A. Benveniste and P. Crepel. Normalite asymptotique: Approximation diffusion pour les algorithmes recursifs: Et applications. Cah. Cent. Etud. Rech. Oper. 23, 3-26, 1981. [294] Albert Benveniste. Introduction a la methode de l’equation differentielle moyenne pour l’etude des algorithmes recursifs. Exemples. Cah. Cent. Etud. Rech. Oper. 22, 219-241, 1980. [295] Regina Benveniste. A note on the set covering problem. J. Oper. Res. Soc., 33(3):261–265, 1982. [296] P. Beraldi and A. Ruszczynski. A branch and bound method for stochastic integer problems under probabilistic constraints. Optimization Methods and Software, 17(3):359–382, 2002. [297] Patrizia Beraldi, Roberto Musmanno, and Cheﬁ Triki. Solving stochastic linear programs with restricted recourse using interior point methods. Comput. Optim. Appl., 15(3):215–234, 2000. [298] Patrizia Beraldi, Roberto Musmanno, and Cheﬁ Triki. Solving stochastic linear programs with restricted recourse using interior point methods. Comput. Optim. Appl., 15(3):215–234, 2000. [299] Patrizia Beraldi and Andrzej Ruszczynski.´ The probabilistic set-covering problem. Oper. Res., 50(6):956–967, 2002. [300] Patrizia Beraldi and Andrzej Ruszczynski.´ Beam search heuristic to solve stochastic integer problems under probabilistic constraints. European J. Oper. Res., 167(1):35–47, 2005. [301] Rustem Berc. Robust optimal policy methods for nonlinear models. In Operations research proceedings 1990, Pap. 19th Annu. Meet. DGOR, Vienna/Austria 1990, 262-271, 1992. [302] B. Bereanu. On stochastic linear programming. Comun. Acad. Republ. popul. Romine 13, 517-522, 1963. [303] B. Bereanu. Stochastic transportation problem. I: Random costs. Comun. Acad. Republ. popul Romine 13, 325-331, 1963. [304] B. Bereanu. Stochastic transportation problem. II: Random consumptions. Comun. Acad. Republ. popul. Romine 13, 333-337, 1963. [305] B. Bereanu. On the distribution of the optimum in stochastic linear programming. An. Univ. Bucuresti, Ser. Sti. Natur., Mat.-Mec. 14, No.2, 41-47, 1965. [306] B. Bereanu. Renewal processes and some stochastic programming problems in economics. SIAM J. Appl. Math. 19, 308-322, 1970. [307] B. Bereanu. Programmation stochastique et quelques-unes de ses applications economiques.´ Publ. Econom´ etriques´ , 5:143–161, 1972. [308] B. Bereanu. On the use of computers in planning under conditions of uncertainty. Computing 15, 11-32, 1975. [309] B. Bereanu. The continuity of the optimum in parametric programming and applications to stochastic programming. J. Optimization Theory Appl., 18(3):319–333, 1976. [310] B. Bereanu. Corrigenda: “Stochastic-parametric linear programs. I.” [Rev. Roumaine Math. Pures Appl. 22 (1977), no. 10, 1367–1380; MR 57 #5092]. Rev. Roumaine Math. Pures Appl., 24(3):509, 1979. [311] B. Bereanu. Linear optimization with mixed indeterminacies in data. Stud. Cerc. Mat., 33(6):601– 610, 1981.

18 [312] B. Bereanu. Minimum risk criterion in stochastic optimization. Econom. Comput. Econom. Cyber- net. Stud. Res., 15(2):31–39, 1981. [313] B. Bereanu and G. Peeters. A ”wait-and-see” problem in stochastic linear programming. An experimental computer code. Cah. Cent. Etud. Rech. Oper. 12, 133-148, 1970. [314] Bernard Bereanu. Quasi-convexity, strictly quasi-convexity and pseudo-convexity of composite objective functions. Rev. Franc¸aise Automat. Informat. Recherche Operationnelle´ , 6(R–1):15–26, 1972. [315] Bernard Bereanu. The Cartesian integration method in stochastic linear programming. In Nu- merische Methoden bei Optimierungsaufgaben (Tagung, Math. Forschungsinst., Oberwolfach, 1971), pages 9–20. Internat. Schriftenreihe Numer. Math., Band 17, Basel, 1973. Birkhauser.¨ [316] Bernard Bereanu. On stochastic linear programming. IV. Some numerical methods and their computer implementation. In Proceedings of the Fourth Conference on Probability Theory (Bras¸ov, 1971), pages 13–36. Editura Acad. R.S.R., Bucharest, 1973. [317] Bernard Bereanu. The Cartesian integration method in stochastic linear programming. In Numer. Meth. Optimierungsaufg., Tagung Oberwolfach 1971, ISNM 17, 9-20 , 1973. [318] Bernard Bereanu. Stable stochastic linear programs and applications. Math. Operationsforsch. Statist., 6(4):593–607, 1975. [319] Bernard Bereanu. The generalized distribution problem of stochastic linear programming. In Sym- posia Mathematica, Vol. XIX (Convegno sulla Programmazione Matematica e sue Applicazioni, INDAM, Roma, 1974), pages 229–267, London, 1976. Academic Press. [320] Bernard Bereanu. On some distribution-free, optimal solutions/bases, in stochastic linear programming. Rev. Roumaine Math. Pures Appl., 21(6):643–657, 1976. [321] Bernard Bereanu. A unifying approach to stochastic linear programming. In Proc. 5th Conf. Probab. Theory, Brasov 1974, 23-31, 1977. [322] Bernard Bereanu. Stochastic-parametric linear programs. I. Revue Roumaine Math. Pur. Appl. 22, 1367-1380, 1977. [323] Bernard Bereanu. Stochastic-parametric linear programs. I. Rev. Roumaine Math. Pures Appl., 22(10):1367–1380, 1977. [324] Bernard Bereanu. Some numerical methods in stochastic linear programming under risk and uncertainty. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 169–205. Academic Press, London, 1980. [325] Bernard Bereanu. Stochastic-parametric linear programs. II. In Recent results in stochastic programming (Proc. Meeting, Oberwolfach, 1979), volume 179 of Lecture Notes in Econom. and Math. Systems, pages 3–20. Springer, Berlin, 1980. [326] Bernard Bereanu. An approach to complexity of optimization linear models. In Proceedings of the Sixth Conference on Probability Theory (Bras¸ov, 1979), pages 385–394, Bucharest, 1981. Ed. Acad. R.S. Romania.ˆ [327] Bernard Bereanu. Programming with composite indeterminacies in data. Methods Oper. Res. 41, 117-120, 1981. [328] Bernard Bereanu. Programming with objective and conventional perturbation in data. In Studies in probability and related topics, pages 21–38. Nagard, Rome, 1983.

19 [329] S.A. Berezin and B.L. Lavrovskij. Probability models of optimization. Textbook. (Veroyatnostnye modeli optimizatsii. Uchebnoe posobie). Ministerstvo Vysshego i Srednego Spetsial’nogo Obrazo- vaniya RSFSR. Novosibirskij Gosudarstvennyj Universitet im. Leninskogo Komsola. Novosibirsk: Novosibirskij Gosudarstvennyj Universitet., 1980. [330] V.A. Bereznev. A stochastic programming problem with probabilistic constraints. Engrg. Cyber- netics, 9(4):613–619 (1972), 1971. [331] V.A. Bereznev. Zwei stochastische Modelle der Planung der Produktion von Halbfabrikaten. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1975, Nr. 1, 26-31, 1975. [332] Menachem Berg. Optimal replacement policies for two-unit machines with increasing running costs. I. Stochastic Processes Appl. 4, 89-106, 1976. [333] Adam J. Berger, John M. Mulvey, and Andrzej Ruszczynski.´ An extension of the DQA algorithm to convex stochastic programs. SIAM J. Optim., 4(4):735–753, 1994. [334] Adam J. Berger, John M. Mulvey, and Andrzej Ruszczynski.´ Restarting strategies for the DQA algorithm. In Large scale optimization (Gainesville, FL, 1993), pages 1–25. Kluwer Acad. Publ., Dordrecht, 1994. [335] J.O. Berger and G. Salinetti. Approximations of Bayes decision problems: the epigraphical approach. Ann. Oper. Res., 56:1–13, 1995. Stochastic programming (Udine, 1992). [336] H. Berglann and S. D. Flam.˚ Stochastic approximation, momentum, and Nash play. In Appli- cations of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 337–345. SIAM, Philadelphia, PA, 2005. [337] Milan Berka. Stochastic methods for global optimization of dynamical systems. Knizniceˇ Odborn. Ved.ˇ Spisu˙ Vysoke.´ Ucenˇ i´ Tech. v Brneˇ B, 111:7–23, 1986. [338] Arjan Berkelaar, Cees Dert, Bart Oldenkamp, and Shuzhong Zhang. A primal-dual decomposition- based interior point approach to two-stage stochastic linear programming. Oper. Res., 50(5):904– 915, 2002. [339] Arjan Berkelaar, Joaquim A. S. Gromicho, Roy Kouwenberg, and Shuzhong Zhang. A primal-dual decomposition algorithm for multistage stochastic convex programming. Math. Program., 104(1, Ser. A):153–177, 2005. [340] E.M. Berkovic. The approximation of two-stage stochastic extremal problems. U.S.S.R. Comput. Math. math. Phys. 1 Nr. 5, 69-88 (1973)., 1971. [341] E.M. Berkovic. Differenzenapproximationen fuer Zweietappenprobleme der stochastischen optimalen Steuerung. Vestnik Moskov. Univ., Ser. I 27, No.3. 43-51, 1972. [342] E.M. Berkovic. Ueber Existenzsaetze in Zweietappenproblemen der stochastischen optimalen Steuerung. Vestnik Moskov. Univ., Ser. I 27, No.2, 64-70, 1972. [343] E.M. Berkovich. The approximation of two-stage stochastic extrem problems. Zh. vycislit. Mat. Mat. Fiz. 11, 1150-1165, 1971. [344] E.M. Berkovich and M.I. Ron’kin. Mathematical models for optimization of reference information services. Autom. Doc. Math. Linguist. 23, No.6, 14-21 translation from Nauchno-Tekh. Inf., Ser. 2 1989, No.11, 19-23 (1989)., 1989. [345] Nils Jacob Berland and Kjetil K. Haugen. Mixing stochastic dynamic programming and scenario aggregation. Ann. Oper. Res., 64:1–19, 1996. Stochastic programming, algorithms and models (Lillehammer, 1994).

20 [346] Oded Berman, Zvi Ganz, and Janet M. Wagner. A stochastic optimization model for planning capacity expansion in a service industry under uncertain demand. Nav. Res. Logist. 41, No.4, 545- 564, 1994. [347] Oded Berman and David Simchi-Levi. Finding the optimal a priori tour and location of a traveling salesman with nonhomogeneous customers. Transp. Sci. 22, No.2, 148-154, 1988. [348] W. Bernard and B. Hiller. Spektralanalyse als Identifikationsproblem. I. Regelungstechnik 30, 393-398, 1982. [349] W. Bernard and B. Hiller. Spektralanalyse als Identifikationsproblem. II. Regelungstechnik 30, 422-427, 1982. [350] Siegfried Berninghaus. Das ”Multi-Armed-Bandit”-Paradigma. Mathematical Systems in Eco- nomics, 92. Koenigstein/Ts.: Verlagsgruppe Athenaeum/Hain/Hanstein., 1984. [351] Marida Bertocchi, Vittorio Moriggia, and Jitka Dupacovˇ a.´ Horizon and stages in applications of stochastic programming in finance. Ann. Oper. Res., 142:63–78, 2006. [352] Dimitri P. Bertsekas and John N. Tsitsiklis. An analysis of stochastic shortest path problems. Math. Oper. Res. 16, No.3, 580-595, 1991. [353] D.P. Bertsekas. Stochastic optimization problems with nondifferentiable cost functionals. J. Opti- mization Theory Appl. 12, 218-231, 1973. [354] Dimitris Bertsimas, Leonid Kogan, and Andrew W. Lo. Hedging derivative securities and incomplete markets: an -arbitrage approach. Oper. Res., 49(3):372–397, 2001. [355] Dimitris Bertsimas and Jose´ Nino-Mora.˜ Restless bandits, linear programming relaxations, and a primal-dual index heuristic. Oper. Res., 48(1):80–90, 2000. [356] Dimitris Bertsimas and Melvyn Sim. Tractable approximations to robust conic optimization problems. Math. Program., 107(1-2, Ser. B):5–36, 2006. [357] Dimitris Bertsimas, Chungpiaw Teo, and Rakesh Vohra. On dependent randomized rounding algorithms. Oper. Res. Lett., 24(3):105–114, 1999. [358] Dimitris Bertsimas and Aurelie´ Thiele. A robust optimization approach to supply chain management. In Integer programming and combinatorial optimization, volume 3064 of Lecture Notes in Comput. Sci., pages 86–100. Springer, Berlin, 2004. [359] B. Betro’ and L. De Biase. A Newton-like method for stochastic optimization. In Towards global optimisation 2, Workshops Varenna 1976 and Bergamo 1977, 269-289, 1978. [360] B. Betro` and F. Schoen. Optimal and sub-optimal stopping rules for the multistart algorithm in global optimization. Math. Programming, 57(3, Ser. A):445–458, 1992. [361] Bruno Betro` and Alessandra Guglielmi. Methods for global prior robustness under generalized moment conditions. In Robust Bayesian analysis, pages 273–293. Springer, New York, 2000. [362] Bruno Betro` and Fabio Schoen. Sequential stopping rules for the multistart algorithm in global optimisation. Math. Programming, 38(3):271–286, 1987. [363] Bruno Betro` and Fabio Schoen. A stochastic technique for global optimization. Comput. Math. Appl., 21(6-7):127–133, 1991. [364] B. Bharath and V. S. Borkar. Robust parameter optimization of hidden Markov models. J. Indian Inst. Sci., 78(2):119–130, 1998. [365] B. Bharath and V. S. Borkar. Stochastic approximation algorithms: overview and recent trends. Sadhan¯ a¯, 24(4-5):425–452, 1999. Chance as necessity.

21 [366] Kabekode V.S. Bhat. Minimization of disjunctive normal forms of fuzzy logic functions. J. Franklin Inst., 311(3):171–185, 1981. [367] S. Bhatnagar, M.C. Fu, and S.I. Marcus. Rate-based ABR flow control using two timescale SPSA. In Proceedings of the SPIE, volume 3841, pages 142–149. The International Society for Optical Engineering, 1999. [368] Sandeep N. Bhatt, Fan R.K. Chung, and Arnold L. Rosenberg. Partitioning circuits for improved testability. Algorithmica, 6(1):37–48, 1991. [369] Malay Bhattacharyya. Joint randomized decisions in chance-constrained programming. J. Oper. Res. Soc. 35, 355-357, 1984. [370] Malay Bhattacharyya. Superiority of randomised decisions in chance constrained programming (CCP). Bull. Inst. Internat. Statist., 52(2):391–406, 1987. [371] Siddhartha Bhattacharyya and Marvin D. Troutt. Genetic search over probability spaces. European J. Oper. Res., 144(2):333–347, 2003. [372] Horst Bialy and Michael Olbrich. Optimierung. Eine Einfuehrung mit Anwendungsbeispielen. Mathematik fuer Ingenieure. Leipzig: VEB Fachbuchverlag., 1975. [373] D. Bienstock and J.F. Shapiro. Optimizing resource acquisition decisions by stochastic programming. Management Science, 34(2):215–229, 1988. [374] S¸. Ilker˙ Birbil, Gul¨ Gurkan,¨ and Ovidiu Listes¸. Solving stochastic mathematical programs with complementarity constraints using simulation. Math. Oper. Res., 31(4):739–760, 2006. [375] J. R. Birge, N. C. P. Edirisinghe, and W. T. Ziemba, editors. Research in stochastic programming. Kluwer Academic Publishers, Dordrecht, 2001. Papers from the 8th International Conference on Stochastic Programming held at the University of British Columbia, Vancouver, BC, August 8–16, 1998, Ann. Oper Res. 100 (2000). [376] J. R. Birge, L. Qi, and Z. Wei. Convergence analysis of some methods for minimizing a nonsmooth convex function. J. Optim. Theory Appl., 97(2):357–383, 1998. [377] J. R. Birge and C. H. Rosa. Modeling investment uncertainty in the costs of global CO2 emission policy. European Journal of Operational Research, 83(3):466–488, 1995. [378] J. R. Birge, S. Takriti, and E. Long. Intelligent unified control of unit commitment and generation allocation. Technical Report 94–26 (revised 1995), Department of Industral and Operations Engineering, The University of Michigan, Ann Arbor, 1994. [379] John Birge and Marc Teboulle. Upper bounds on the expected value of a convex function using gradient and conjugate function information. Math. Oper. Res., 14(4):745–759, 1989. [380] John R. Birge. The value of the stochastic solution in stochastic linear programs with fixed recourse. Math. Programming, 24(3):314–325, 1982. [381] John R. Birge. Aggregation bounds in stochastic linear programming. Math. Programming, 31(1):25–41, 1985. [382] John R. Birge. Decomposition and partitioning methods for multistage stochastic linear programs. Oper. Res., 33(5):989–1007, 1985. [383] John R. Birge. Stochastic programming: optimizing the uncertain. In Optimization, Vol. 1, 2 (Singapore, 1992), pages 613–632. World Sci. Publishing, River Edge, NJ, 1992. [384] John R. Birge. Models and model value in stochastic programming. Ann. Oper. Res., 59:1–18, 1995. Models for planning under uncertainty.

22 [385] John R. Birge. Stochastic programming computation and applications. INFORMS J. Comput., 9(2):111–133, 1997. [386] John R. Birge and M.A.H. Dempster. Optimal match-up strategies in stochastic scheduling. Dis- crete Appl. Math. 57, No.2-3, 105-120, 1995. [387] John R. Birge and M.A.H. Dempster. Stochastic programming approaches to stochastic scheduling. J. Global Optim., 9(3-4):417–451, 1996. Optimization applications in scheduling theory. [388] John R. Birge and Jose´ H. Dula.´ Bounding separable recourse functions with limited distribution information. Ann. Oper. Res., 30(1-4):277–298, 1991. Stochastic programming, Part I (Ann Arbor, MI, 1989). [389] John R. Birge and François Louveaux. Introduction to stochastic programming. Springer-Verlag, New York, 1997. [390] John R. Birge and François V. Louveaux. A multicut algorithm for two-stage stochastic linear programs. European J. Oper. Res., 34(3):384–392, 1988. [391] John R. Birge, Stephen M. Pollock, and Liqun Qi. A quadratic recourse function for the two-stage stochastic program. In Progress in optimization (Perth, 1998), pages 109–121. Kluwer Acad. Publ., Dordrecht, 2000. [392] John R. Birge and Li Qun Qi. Computing block-angular Karmarkar projections with applications to stochastic programming. Management Sci., 34(12):1472–1479, 1988. [393] John R. Birge and Li Qun Qi. Semiregularity and generalized subdifferentials with applications to optimization. Math. Oper. Res., 18(4):982–1005, 1993. [394] John R. Birge and Li Qun Qi. Continuous approximation schemes for stochastic programs. Ann. Oper. Res., 56:15–38, 1995. Stochastic programming (Udine, 1992). [395] John R. Birge and Li Qun Qi. Subdifferential convergence in stochastic programs. SIAM J. Optim., 5(2):436–453, 1995. [396] John R. Birge and Charles H. Rosa. Parallel decomposition of large-scale stochastic nonlinear programs. Ann. Oper. Res., 64:39–65, 1996. Stochastic programming, algorithms and models (Lillehammer, 1994). [397] John R. Birge and Robert L. Smith. Random procedures for nonredundant constraint identification in stochastic linear programs. Amer. J. Math. Management Sci., 4(1-2):41–70, 1984. Statistics and optimization : the interface. [398] John R. Birge and Samer Takriti. Successive approximations of linear control models. SIAM J. Control Optim., 37(1):165–176 (electronic), 1999. [399] John R. Birge and Stein W. Wallace. Refining bounds for stochastic linear programs with linearly transformed independent random variables. Oper. Res. Lett., 5(2):73–77, 1986. [400] John R. Birge and Stein W. Wallace. A separable piecewise linear upper bound for stochastic linear programs. SIAM J. Control Optim., 26(3):725–739, 1988. [401] John R. Birge and Roger J.-B. Wets. Approximations and error bounds in stochastic programming. In Inequalities in statistics and probability (Lincoln, Neb., 1982), volume 5 of IMS Lecture Notes- Monograph Ser., pages 178–186, Hayward, Calif., 1984. Inst. Math. Statist. [402] John R. Birge and Roger J.-B. Wets. Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse. Math. Programming Stud., 27:54– 102, 1986. Stochastic programming 84. I.

23 [403] John R. Birge and Roger J.-B. Wets. Computing bounds for stochastic programming problems by means of a generalized moment problem. Math. Oper. Res., 12(1):149–162, 1987. [404] John R. Birge and Roger J.-B. Wets. Sublinear upper bounds for stochastic programs with recourse. Math. Programming (Ser. A), 43(2):131–149, 1989. [405] J.R. Birge. An L-shaped method computer code for multistage stochastic linear programs. In Numerical techniques for stochastic optimization, Springer Ser. Comput. Math. 10, 255-266, 1988. [406] J.R. Birge. Exhaustible resource models with uncertain returns from exploration investment. In Numerical techniques for stochastic optimization, Springer Ser. Comput. Math. 10, 481-488, 1988. [407] J.R. Birge. The relationship between the L-shaped method and dual basis factorization for stochastic linear programming. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 267–272. Springer, Berlin, 1988. [408] J.R. Birge and C.J. Donohue. An upper bound on the expected value of a non-increasing convex function with convex marginal return functions. Operations Research Letters 18:213-221, 1996. [409] J.R. Birge, C.J. Donohue, D.F. Holmes, and O.G. Svintsitski. A parallel implementation of the nested decomposition algorithm for multistage stochastic linear programs. Mathematical Program- ming, 75(2):327–352, 1996. [410] J.R. Birge and D.F. Holmes. Efﬁcient solution of two-stage stochastic linear programs using interior point methods. Comput. Optim. Appl., 1(3):245–276, 1992. [411] J.R. Birge and C.H. Rosa. Incorporating investment uncertainty into greenhouse policy models. The Energy Journal 17:79-90, 1996. [412] J.R. Birge and C.H. Rosa. Parallel decomposition of large scale stochastic nonlinear programs. Annals of Operations Research, 64:39–65, 1996. [413] J.R. Birge and R.J.-B. Wets, editors. Stochastic programming. Part I. J.C. Baltzer A.G., Basel, 1991. Papers from the Fifth International Conference held at the University of Michigan, Ann Arbor, Michigan, August 13–18, 1989, Ann. Oper. Res. 30 (1991), no. 1-4. [414] J.R. Birge and R.J.-B. Wets, editors. Stochastic programming. Part II. J.C. Baltzer A.G., Basel, 1991. Papers from the Fifth International Conference held at the University of Michigan, Ann Arbor, Michigan, August 13–18, 1989, Ann. Oper. Res. 31 (1991), no. 1-4. [415] M. P. Biswal, N. P. Sahoo, and Duan Li. Probabilistic linearly constrained programming problems with lognormal random variables. Opsearch, 42(1):70–76, 2005. [416] Gabriel R. Bitran, Elizabeth A. Haas, and Hirofumi Matsuo. Production planning of style goods with high setup costs and forecast revisions. Oper. Res. 34, 226-236, 1986. [417] G.R. Bitran and D. Tirupati. Hierarchical production planning. In S.C. Graves, A.H.G. Rinnooy Kan, and P.H. Zipkin, editors, Handbooks on Operations Research and Management Science, volume 4, pages 523–568. North-Holland, Amsterdam, 1993. [418] H. Bjørstad, D. Haugland, and R. Helming. A stochastic model for gasoline blending. In M. Breton and G. Zaccour, editors, Advances in Operations Research in the Oil and Gas Industry, pages 137– 142, 1991. [419] Charles Blair. Random inequality constraint systems with few variables. Math. Programming, 35(2):135–139, 1986. [420] Roger A. Blau. Erratum: N job, one machine sequencing problems under uncertainty. Management Sci., Theory 20, 896-899, 1974.

24 [421] Roger A. Blau. Stochastic programming and decision analysis: an apparent dilemma. Management Sci., 21(3):271–276, 1974. [422] Jean-Marie Blin, King-Sun Fu, Andrew B. Whinston, and Kenneth B. Moberg. Pattern recognition in micro-economics. J. Cybernetics 3, Nr. 4, 17-27, 1973. [423] Jorgen¨ Blomvall and Per Olov Lindberg. A Riccati-based primal interior point solver for multistage stochastic programming. European J. Oper. Res., 143(2):452–461, 2002. Interior point methods (Budapest, 2000). [424] Jorgen¨ Blomvall and Per Olov Lindberg. A Riccati-based primal interior point solver for multistage stochastic programming—extensions. Optim. Methods Softw., 17(3):383–407, 2002. Stochastic programming. [425] Jorgen¨ Blomvall and Alexander Shapiro. Solving multistage asset investment problems by the sample average approximation method. Math. Program., 108(2-3, Ser. B):571–595, 2006. [426] J. A. Bloom. Solving an electricity generation capacity expansion planning problem by generalized Benders’ decomposition. Operations Research, 31:84–100, 1983. [427] Lawrence Blume, David Easley, and Maureen O’Hara. Characterization of optimal plans for stochastic dynamic programs. J. Econ. Theory 28, 221-234, 1982. [428] John Board, Charles Sutcliffe, and William T. Ziemba. The application of operations research techniques to ﬁnancial markets. Stochastic Programming E-Print Series, http://www.speps. org, 1999. [429] I.I. Bockareva.ˇ The algorithm for the solution of a certain class of stochastic programming problems with probabilistic constraints. Optimal. Planirovanie, 16:10–15, 1970. [430] C.E. Bocvarova. Optimierung der Struktur eines Flaecheninhalts fuer verschiedene Kulturen auf einer Flaeche ohne Bedarf an Bewaesserung und auf einem vorgegebenen Massiv, der aus einer nichteinregulierten Quelle bei stochastischen Schwankungen der Wasserverhaeltnisse bewaessert wird. Optimizacija 17(34), 67-72, 1975. [431] C.E. Bocvarova. Ueber die Wahl der garantierten Wahrscheinlichkeiten in Problemen der stochastischen Programmierung mit Wahrscheinlichkeitsbeschraenkungen. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1975, Nr. 6, 47-54, 1975. [432] C.E. Bocvarova. Ueber ein stochastisches Modell der Bestimmung der Optimalzahl der staendig beschaeftigten Arbeiter und der Struktur der Produktion eines landwirtschaftlichen Unternehmens. Optimizacija 16(33), 73-83, 1975. [433] V.A. Bodner, N.E. Rodnishchev, and E.P. Yurikov. Optimizatsiya terminal’ nykh stokhasticheskikh sistem. “Mashinostroenie”, Moscow, 1987. [434] C. Guus E. Boender and H. Edwin Romeijn. Stochastic methods. In Handbook of global optimization, volume 2 of Nonconvex Optim. Appl., pages 829–869. Kluwer Acad. Publ., Dordrecht, 1995. [435] C.G.E. Boender and A.H.G. Rinnooy Kan. Bayesian stopping rules for multistart global optimization methods. Math. Programming, 37(1):59–80, 1987. [436] C.G.E. Boender, A.H.G. Rinnooy Kan, L. Stougie, and G.T. Timmer. Global optimization: a stochastic approach. In Numerical techniques for stochastic systems (Conf., Gargnano, 1979), pages 387–394, Amsterdam, 1980. North-Holland. [437] C.G.E. Boender, A.H.G. Rinnooy Kan, and C. Vercellis. Stochastic optimization methods. In Stochastics in combinatorial optimization (Udine, 1986), pages 94–112. World Sci. Publishing, Singapore, 1987.

25 [438] Juergen Boettcher. Local decomposition for linear programs with dual block-angular structure. Methods Oper. Res. 58, 15-25, 1989. [439] Alexander Boﬁnger. Numerical determination of response surface points with minimal absolute value for a lower bound estimate of multinormal integrals—gradient algorithms and their convergence. In Stochastic optimization techniques (Neubiberg/Munich, 2000), volume 513 of Lecture Notes in Econom. and Math. Systems, pages 59–78. Springer, Berlin, 2002. [440] I.P. Boglaev. Finding a feasible optimal program in the problem of programmed control under disturbances. Autom. Remote Control 43, 1315-1321 translation from Avtom. Telemekh. 1982, No.10, 107-114 (1982)., 1983. [441] M.G.V. Bogle and M.J. O’Sullivan. The effect of storage carryover on plant expansion planning. J. Oper. Res. Soc. 31, 319-324, 1980. [442] V.A. Bol’shakov. Local-optimization algorithms of group supplies control. Podstawy Sterowania 13, 165-176, 1983. [443] P. Bonami and M.A. Lejeune. An exact solution approach for portfolio optimization problems under stochastic and integer constraints. Stochastic Programming E-Print Series, http://www. speps.org, 2007. [444] I.M. Bondar’. Application of stochastic programming methods in the construction of mathematical models of complex systems under conditions of incomplete information. In Methods of operations research and of reliability theory in systems analysis (Russian), pages 52–63, Kiev, 1977. Akad. Nauk Ukrain. SSR Inst. Kibernet. [445] V.A. Bondarenko and A.A. Korotkin. Analysis of discrete optimization algorithms using incomplete information. Zh. Vychisl. Mat. i Mat. Fiz., 21(3):783–786, 814, 1981. [446] J.G. Boon, J.D. Pinter, and L. Somlyody. A new stochastic approach for controlling point source river pollution. In Proc. 3rd Scientiﬁc Assembly of the International Association for Hydrologic Sciences (Baltimore, 1989), pages 241–249. IAHS Publications 180, 1989. [447] A. E. Bopp, V. R. Kannan, S. W. Palocsay, and S. P. Stevens. An optimization model for planning natural gas purchases, transportation, storage and deliverability. Omega, International Journal of Management Science, 24(5):511–522, 1996. [448] A.N. Bordunov, A.I. Yastremskij, and N. Utenliev. On duality relations and optimality conditions in linear problems of stochastic programming with discretely distributed random variables. Issled. Oper. ASU 29, 27-37, 1987. [449] N.N. Bordunov. Optimality conditions for multistep control of stochastic convex mappings. Cy- bernetics, 19(1):48–56, 1983. [450] N.N. Bordunov. Dynamic programming and conditions of optimality of control of stochastic convex mappings. Cybernetics, 20(2):233–239, 1984. [451] N.N. Bordunov. Extremum conditions for a multistage problem of stochastic programming with smooth constraints. Kibernetika (Kiev), 6:iii, 77–82, 135, 1984. [452] N.N. Bordunov. Convex multivalued mappings and stochastic models of the dynamics of economic systems. In Stochastic optimization, Proc. Int. Conf., Kiev/USSR 1984, Lect. Notes Control Inf. Sci. 81, 309-313, 1986. [453] N.N. Bordunov. Dynamical optimization models under conditions of uncertainty: multistage problems of stochastic programming (from IIASA reports). (Dinamicheskie optimizatsionnye modeli v usloviyakh neopredelennosti: mnogoehtapnye zadachi stokhasticheskogo programmirovaniya (po materialam IIASA)). Institut Kibernetiki AN USSR, Kiev, 1991.

26 [454] N.N. Bordunov, N. Uteuliev, and A.I. Yastremskii. Duality relations and conditions for optimality in nonlinear stochastic programming problems. Issled. Operatsii i ASU, 31:19–22, 112, 1988. [455] N.N. Bordunov, N. Uteuliev, and A.I. Yastremskii. Multistage problems in stochastic linear programming with discrete distributions. Vestnik Kiev. Univ. Model. Optim. Slozhn. Sist., 7:90–95, 109, 1988. [456] N.N. Bordunov and N. Uteuliyev. The subdifferential form of optimality conditions for convex multistage stochastic programming problems. Soviet J. Automat. Inform. Sci., 21(3):52–56 (1989), 1988. [457] N.N. Bordunov, A.I. Yastremskii, and N. Uteuliev. Duality relations and conditions for optimality in linear problems of stochastic programming with discretely distributed random variables. Issled. Operatsii i ASU, 29:27–37, 114, 1987. [458] N.N. Bordunov, A.I. Yastremskii, and N. Uteuliev. Stochastic programming problems with discrete distributions. Kibernetika (Kiev), 3:121–122, 135, 1988. [459] Karl-Heinz Borgwardt. Untersuchungen zur Asymptotik der mittleren Schrittzahl von Simplexver- fahren in der linearen Optimierung., 1977. [460] A.I. Borisenko, Ya.I. Zelyk, V.M. Kuntsevich, and M.M. Lychak. The convergence of a matrix stochastic control algorithm for a static object with constrained controls. Sov. J. Autom. Inf. Sci. 18, No.2, 41-49 translation from Avtomatika 1985, No.2, 43-51 (1985)., 1985. [461] A. B. Borison, P. A. Morris, and S. S. Oren. A state-of-the-world decomposition approach to dynamics and uncertainty in electric utility generation expansion planning. Operations Research, 32:1052–1068, 1984. [462] Vivek S. Borkar. Pathwise recurrence orders and simulated annealing. J. Appl. Probab., 29(2):472– 476, 1992. [463] N.I. Borodyanskii. Limit theorems for some problems of stochastic optimization. Issled. Operatsii i ASU, 23:16–19, 138, 1984. [464] A.V. Borshchevskii. On the problem of identification of parameters of nonlinear models by the method of least absolute values. In Investigation of methods for solving extremal problems (Rus- sian), pages 3–7, i, Kiev, 1986. Akad. Nauk Ukrain. SSR Inst. Kibernet. [465] M.Z. Borshchevskij, I.V. German, and L.M. Shevchuk. Multistep process of taking decisions under conditions of uncertainty. In Approximate methods in the solution of operator equations and their applications, Collect. Artic., Irkutsk 1982, 182-193, 1982. [466] Jurgen¨ Bottcher.¨ Stochastische lineare Programme mit Kompensation, volume 115 of Mathemati- cal Systems in Economics. Athenaum¨ Verlag GmbH, Frankfurt am Main, 1989. [467] M. Bouhadi, R. Ellaia, and J. E. Souza de Cursi. Stochastic perturbation methods for affine restrictions. In Advances in convex analysis and global optimization (Pythagorion, 2000), volume 54 of Nonconvex Optim. Appl., pages 487–499. Kluwer Acad. Publ., Dordrecht, 2001. [468] E.-K. Boukas, A. Haurie, and P. Michel. An optimal control problem with a random stopping time. J. Optim. Theory Appl., 64(3):471–480, 1990. [469] Craig Boutilier, Richard Dearden, and Moises´ Goldszmidt. Stochastic dynamic programming with factored representations. Artificial Intelligence, 121(1-2):49–107, 2000. [470] C. Bouza, editor. Stochastic Programming: The State of the Art. 1993. Revista Investigacion´ Operational 14, No.2–3.

27 [471] Carlos Bouza. Bootstrap estimation of the bound of the approximation error in stochastic programming with complete ﬁxed recourse. Investigacion´ Oper., 13(3):226–232, 1992. [472] Carlos Bouza. Approximation of the value of the optimal solution in stochastic programming. Investigacion´ Oper., 15(1):13–33, 1994. [473] Carlos Bouza and Sira Allende. Use of L-estimate approximations for solving chance constrained programs. Investigacion´ Oper., 14(2-3):119–126, 1993. Workshop on Stochastic Optimization: the State of the Art (Havana, 1992). [474] Carlos Bouza Herrera. Bounding the expected approximation error in stochastic linear programming with complete ﬁxed recourse. In System modelling and optimization (Zurich, 1991), volume 180 of Lecture Notes in Control and Inform. Sci., pages 541–545. Springer, Berlin, 1992. [475] Carlos Bouza Herrera. Use of bootstrap approximations for solving stochastic linear programming problems. Investigacion´ Oper., 16(1-2):3–10, 1995. [476] Carlos Bouza Herrera and Sira Allende Alonso. Density function estimation and the approximation of convergence rates in stochastic linear programming. Investigacion´ Oper., 10(3):135–140, 1989. [477] Carlos Bouza Herrera and Sira Allende Alonso. Bounding the variance of the approximation error. Investigacion´ Oper., 11(1):29–36, 1990. [478] Aziz Bouzaher. Symmetric QP and linear programming under primal-dual uncertainty. Oper. Res. Lett. 6, 221-225, 1987. [479] Aziz Bouzaher and Susan Offutt. A stochastic linear programming model for corn residue production. J. Oper. Res. Soc. 43, No.9, 843-857, 1992. [480] Bruce L. Bowerman and Anne B. Koehler. An optimal policy for sampling from uncertain distributions. Comm. Statist. A—Theory Methods, 7(11):1041–1051, 1978. [481] H. Woods Bowman and Anne Marie Laporte. Stochastic optimization in recursive equation systems with random parameters with an application to control of the money supply. In Studies in Bayesian econometrics and statistics (in honor of Leonard J. Savage), pages 441–462. Contributions to Eco- nomic Analysis, No. 86, North-Holland, Amsterdam, 1975. Reprinted from Ann. Econom. Social Measurement 1 (1972), 419–435. [482] Friedrich Bozena and Klaus Tammer. Untersuchungen zur Stabilitaet einiger Ersatzprobleme der stochastischen Optimierung in bezug auf Aenderungen des zugrunde gelegten Zufallsvektors. Wiss. Z. Humboldt-Univ. Berlin, Math.-Naturwiss. Reihe 30, 373-376, 1981. [483] Steven J. Brams and D. Marc Kilgour. The box problem: to switch or not to switch. Math. Mag., 68(1):27–34, 1995. [484] Andries S. Brandsma and A.J. Hughes Hallett. A method for optimising risk sensitive decisions. Rev. Belg. Stat. Inf. Rech. Oper. 24, No.3, 30-43, 1983. [485] Andrzej Brandt, Stefan Jendo, and Wojciech Marks. Probabilistic approach to reliability-based optimal structural design. Rozpr. Inz. 32, 57-74, 1984. [486] Andrzej M. Brandt, Wojciech Dzieniszewski, Stefan Jendo, Wojciech Marks, Stefan Owczarek, and Zbigniew Wasiutynski. Criteria and methods of structural optimization. Ed. by Andrzej M. Brandt. Transl. from the Polish by Antoni Pol. Dordrecht/Boston/Lancaster: Martinus Nijhoff Publishers, 1986. [487] C. Brasca, F. Romeo, R. Scattolini, and N. Schiavoni. Reduced-order modelling of large-scale stochastic systems: a two-level Newton-like algorithm. In Control applications of nonlinear programming and optimization, Coll. Pap., 2nd IFAC Workshop, Oberpfaffenhofen/Ger. 1980, 44-54, 1980.

28 [488] Michele` Breton and Saeb El Hachem. Algorithms for the solution of a large-scale single-controller stochastic game. In Advances in dynamic games and applications (Geneva, 1992), volume 1 of Ann. Internat. Soc. Dynam. Games, pages 195–216. Birkhauser¨ Boston, Boston, MA, 1994. [489] Michele` Breton and Saeb El Hachem. Algorithms for the solution of stochastic dynamic minimax problems. Comput. Optim. Appl., 4(4):317–345, 1995. [490] Michele` Breton and Saeb El Hachem. A scenario aggregation algorithm for the solution of stochastic dynamic minimax problems. Stochastics Stochastics Rep., 53(3-4):305–322, 1995. [491] D.F. Broens and W.K. Klein Haneveld. Investment evaluation based on the commercial scope. the production of natural gas. Annals of Operations Research, 59:195–226, 1995. [492] D.M. Brooks and C.T. Leondes. Use of isolated forecasts in Markov decision processes with imperfect information. AIIE Trans., 6:244–251, 1974. [493] George W. Brown. Recursive sets of rules in statistical decision processes. In Statist. Papers in Honor of George W. Snedecor, 59-75, 1972. [494] Gerald G. Brown and Herbert C. Rutemiller. Means and variances of stochastic vector products with applications to random linear models. Manage. Sci. 24, 210-216, 1977. [495] Lawrence D. Brown. Closure theorems for sequential-design processes. In Statistical decision theory and related topics II, Proc. Symp., West Lafayette/Indiana 1976, 57-91, 1977. [496] Lawrence D. Brown and Bharat T. Doshi. Existence of optimal policies in stochastic dynamic programming. Probab. Math. Statist., 1(2):171–184 (1981), 1980. [497] R. Brunelli and G.P. Tecchiolli. Stochastic minimization with adaptive memory. J. Comput. Appl. Math., 57(3):329–343, 1995. [498] Giordano Bruno and Angelo Gilio. Application of the simplex method to the fundamental theorem for the probabilities in the subjective theory. Statistica (Bologna), 40(3):337–344, 1980. [499] Noel A. Bryson and Saul I. Gass. Solving discrete stochastic linear programs with simple recourse by the dualplex algorithm. Comput. Oper. Res. 21, No.1, 11-17, 1994. [500] Z. Bubnicki. Optimization problems in large-scale systems modelling and identiﬁcation. In Large scale systems: theory and applications, Proc. IFAC/IFORS Symp., Warsaw/Pol. 1983, IFAC Proc. Ser. 10, 411-416, 1984. [501] Z. Bubnicki, M. Staroswiecki,´ and A. Lebrun. Stochastic approach to the two-level optimization of the complex of operations. In Optimization techniques (Proc. Ninth IFIP Conf., Warsaw, 1979), Part 2, volume 23 of Lecture Notes in Control and Information Sci., pages 281–290. Springer, Berlin, 1980. [502] C. S. Buchanan, K. I. M. McKinnon, and G. K. Skondras. The recursive deﬁnition of stochastic linear programming problems within an algebraic modeling language. Ann. Oper Res., 104:15–32 (2002), 2001. Modeling languages and systems. [503] J.J. Buckley. Fuzzy programming and the Pareto optimal set. Fuzzy Sets Syst. 10, 57-63, 1983. [504] J.J. Buckley. Possibility and necessity in optimization. Fuzzy Sets and Systems, 25(1):1–13, 1988. [505] J.J. Buckley. Solving possibilistic linear programming problems. Fuzzy Sets and Systems, 31(3):329–341, 1989. [506] J.J. Buckley. Stochastic versus possibilistic multiobjective programming. In Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, volume 6 of Theory Decis. Lib. Ser. D System Theory Knowledge Engrg. Probl. Solving, pages 353–364. Kluwer Acad. Publ., Dordrecht, 1990.

29 [507] G. Buehler. Informationsbedarf bei Produktions-Lagerhaltungs-Modellen. In Proc. Oper. Res. 6, DGOR, Pap. ann. Meet. 1976, 380-389, 1976. [508] W. Buehler. Ein kombiniertes Kompensations-Chance-Constrained Modell der stochastischen linearen Programmierung. In Operations Res.-Verf. 12, IV. Oberwolfach-Tag. Operations Res. 1971, 61-68 , 1972. [509] W. Buehler. Zur Loesung eines Zwei-Stufen-Risiko Modells der stochastischen linearen Opti- mierung. In Proc. Oper. Res., DGU Ann. Meet. 1971, 355-370, 1972. [510] Wolfgang Buehler. Stochastische lineare Optimierung ueber halbgeordneten Ereignismengen. In Oper. Res. Verf. 21, VII. Oberwolfach-Tag. Oper. Res. 1974, 48-50, 1975. [511] Wolfgang Buhler.¨ Stochastische lineare Optimierung uber¨ halbgeordneten Ereignismengen. In Siebente Oberwolfach-Tagung uber¨ Operations Research (1974), pages 48–50. Operations Re- search Verfahren, Band XXI, Meisenheim am Glan, 1975. Hain. [512] Jozsef´ Bukszar.´ Lower and upper bounds on the probability of the union of some events with applications. In Optimization theory (Matrah´ aza,´ 1999), volume 59 of Appl. Optim., pages 33–43. Kluwer Acad. Publ., Dordrecht, 2001. [513] Jozsef Bukszar, Rene´ Henrion, Mihaly Hujter, and Tamas Szantai. Polyhedral inclusion-exclusion. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [514] Jozsef´ Bukszar´ and Andras´ Prekopa.´ Probability bounds with cherry trees. Math. Oper. Res., 26(1):174–192, 2001. [515] Jozsef´ Bukszar´ and Tamas´ Szantai.´ Probability bounds given by hypercherry trees. Optim. Methods Softw., 17(3):409–422, 2002. Stochastic programming. [516] D. W. Bulger, D. Alexander, W. P. Baritompa, G. R. Wood, and Z. B. Zabinsky. Expected hitting times for backtracking adaptive search. Optimization, 53(2):189–202, 2004. [517] D. W. Bulger and G. R. Wood. Hesitant adaptive search for global optimisation. Math. Program- ming, 81(1, Ser. A):89–102, 1998. [518] O. Bunke. Einige Hilfsmittel zur Loesung statistischer Probleme bei der linearen und nichtlinearen Optimierung. Monatsber. Deutsch. Akad. Wiss. Berlin 8, 699-703, 1966. [519] O. Bunke. Einige statistische Probleme und Methoden bei der linearen und nichtlinearen Opti- mierung. In Operationsforsch. Math. Statistik 1 (Schriftenr. Inst. Math. Dtsch. Akad. Wiss. Berlin, Reihe B, H. 8), 19-34, 1968. [520] O. Bunke. Ueber die Guete der linearen und nichtlinearen Optimierung bei geschaetzten Parame- tern. In Operationsforsch. Math. Statistik 1 (Schriftenr. Inst. Math. Dtsch. Akad. Wiss. Berlin, Reihe B, H. 8), 9-18, 1968. [521] Derek W. Bunn and Spiros N. Paschentis. A model-switching criterion for a class of stochastic linear programs. Appl. Math. Modelling, 5(5):336–340, 1981. [522] Derek W. Bunn and Spiros N. Paschentis. Development of a stochastic model for the economic dispatch of electric power. Eur. J. Oper. Res. 27, 179-191, 1986. [523] Rainer E. Burkard and Helidon Dollani. Robust location problems with pos/neg weights on a tree. Networks, 38(2):102–113, 2001. [524] A. Burkauskas. On convexity problems of the probabilistic constrained stochastic programming problems. Alkalmaz. Mat. Lapok, 12(1-2):77–90, 1986.

30 [525] V.N. Burkov and D.A. Novikov. Optimal stimulation mechanisms in an active system with probabilistic uncertainty. II. Avtomat. i Telemekh., 10:121–126, 1995. [526] F.V. Burshtein and E.` S. Korelov. Multicriteria decision making problems with indeterminacy and risk. In Theoretical cybernetics (Russian), pages 143–148, Tbilisi, 1980. “Metsniereba”. [527] K.V. Bury. Design optimization under cost uncertainty and risk aversion. INFOR, Canadian J. operat. Res. Inform. Processing 14, 250-258, 1976. [528] J. C. Butler and J. S. Dyer. Optimizing natural gas flows with linear programming and scenarios. Decision Sciences, 30(2):563–580, 1999. [529] Dan Butnariu. Fixed points for fuzzy mappings. Fuzzy Sets and Systems, 7(2):191–207, 1982. [530] Dan Butnariu. Corrigendum: “Fixed points for fuzzy mappings” [Fuzzy Sets and Systems 7 (1982), no. 2, 191–207; MR 83d:90150]. Fuzzy Sets and Systems, 12(1):93, 1984. [531] Dan Butnariu, Yair Censor, and Simeon Reich. Iterative averaging of entropic projections for solving stochastic convex feasibility problems. Comput. Optim. Appl., 8(1):21–39, 1997. [532] Dan Butnariu, Alfredo N. Iusem, and Regina S. Burachik. Iterative methods of solving stochastic convex feasibility problems and applications. Comput. Optim. Appl., 15(3):269–307, 2000. [533] Dan Butnariu, Alfredo N. Iusem, and Regina S. Burachik. Iterative methods of solving stochastic convex feasibility problems and applications. Comput. Optim. Appl., 15(3):269–307, 2000. [534] Dan Butnariu and Elena Resmerita. The outer Bregman projection method for stochastic feasibility problems in Banach spaces. In Inherently parallel algorithms in feasibility and optimization and their applications (Haifa, 2000), volume 8 of Stud. Comput. Math., pages 69–86. North-Holland, Amsterdam, 2001. [535] Richard H. Byrd, Thomas Derby, Elizabeth Eskow, Klaas P.B. Oldenkamp, and Robert B. Schnabel. A new stochastic/perturbation method for large-scale global optimization and its application to water cluster problems. In Large scale optimization (Gainesville, FL, 1993), pages 68–81. Kluwer Acad. Publ., Dordrecht, 1994. [536] R. Caballero, E. Cerda,´ M. M. Munoz,˜ L. Rey, and I. M. Stancu-Minasian. Efficient solution concepts and their relations in stochastic multiobjective programming. J. Optim. Theory Appl., 110(1):53–74, 2001. [537] R. Caballero, E. Cerda, M. M. Munoz,˜ and L. Rey. Analysis and comparisons of some solution concepts for stochastic programming problems. Top, 10(1):101–123, 2002. [538] Rafael Caballero, Emilio Cerda,´ María del Mar Munoz,˜ and Lourdes Rey. Stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems. European J. Oper. Res., 158(3):633–648, 2004. [539] Yong Xin Cai, Bao Liu, and Ji Song Kou. A novel method for solving chance constrained stochastic programming problems. J. Tianjin Univ., 4:50–57, 1985. [540] M. Cain and M.L.R. Price. Optimal mixture choice. J. R. Stat. Soc., Ser. C 35, 1-7, 1986. [541] R. Cairoli and Robert C. Dalang. Sequential stochastic optimization. Wiley Series in Probability and Statistics: Probability and Statistics. John Wiley & Sons Inc., New York, 1996. A Wiley- Interscience Publication. [542] G. C. Calafiore and L. El Ghaoui. On distributionally robust chance-constrained linear programs. J. Optim. Theory Appl., 130(1):1–22, 2006.

31 [543] Giuseppe Calafiore and Boris T. Polyak. Stochastic algorithms for exact and approximate feasibility of robust LMIs. IEEE Trans. Automat. Control, 46(11):1755–1759, 2001. [544] J.R. Callahan and C.R. Bector. Optimization with general stochastic objective functions. In Pro- ceedings of the Third Manitoba Conference on Numerical Mathematics (Winnipeg, Man., 1973), pages 127–137, Winnipeg, Man., 1974. Utilitas Math. [545] J.R. Callahan and C.R. Bector. Optimization with general stochastic objective functions. Z. Angew. Math. Mech., 55(9):528–530, 1975. [546] J. Calvin and A. Zilinskas.ˇ On the convergence of the P-algorithm for one-dimensional global optimization of smooth functions. J. Optim. Theory Appl., 102(3):479–495, 1999. [547] J. Calvin and A. Zilinskas.ˇ One-dimensional P-algorithm with convergence rate O.n−3+/ for smooth functions. J. Optim. Theory Appl., 106(2):297–307, 2000. [548] J. Calvin and A. Zilinskas.ˇ One-dimensional P-algorithm with convergence rate O.n−3+/ for smooth functions. J. Optim. Theory Appl., 106(2):297–307, 2000. [549] J. M. Calvin and A. Zilinskas. One-dimensional global optimization for observations with noise. Comput. Math. Appl., 50(1-2):157–169, 2005. [550] James M. Calvin. Non-adaptive coverings for optimization of Gaussian random fields. In Monte Carlo and quasi-Monte Carlo methods in scientific computing (Las Vegas, NV, 1994), volume 106 of Lecture Notes in Statist., pages 149–157. Springer, New York, 1995. [551] James M. Calvin. Average performance of a class of adaptive algorithms for global optimization. Ann. Appl. Probab., 7(3):711–730, 1997. [552] James M. Calvin. Nonadaptive univariate optimization for observations with noise. In Models and algorithms for global optimization, volume 4 of Springer Optim. Appl., pages 185–192. Springer, New York, 2007. [553] James M. Calvin and Antanas Zilinskas.ˇ On the choice of statistical model for one-dimensional P-algorithms. Control Cybernet., 29(2):555–565, 2000. [554] James M. Calvin and Antanas Zilinskas.ˇ On convergence of a P-algorithm based on a statistical model of continuously differentiable functions. J. Global Optim., 19(3):229–245, 2001. Interna- tional Workshop on Global Optimization, Part 2 (Firenze, 1999). [555] David Canning. Average behavior in learning models. J. Econom. Theory, 57(2):442–472, 1992. [556] X. R. Cao. Single sample path-based optimization of Markov chains. J. Optim. Theory Appl., 100(3):527–548, 1999. [557] Xi-Ren Cao. Convergence of parameter sensitivity estimates in a stochastic experiment. IEEE Trans. Autom. Control AC-30, 845-853, 1985. [558] Andrew Caplin and John Leahy. The recursive approach to time inconsistency. J. Econom. Theory, 131(1):134–156, 2006. [559] Robert Carbone. Public facilities location under stochastic demand. INFOR—Canad. J. Opera- tional Res. and Information Processing, 12:261–270, 1974. [560] David R. Carino,˜ David H. Myers, and William T. Ziemba. Concepts, technical issues, and uses of the Russell-Yasuda Kasai financial planning model. Oper. Res., 46(4):450–462, 1998. [561] David R. Carino˜ and William T. Ziemba. Formulation of the Russell-Yasuda Kasai financial planning model. Oper. Res., 46(4):433–449, 1998.

32 [562] D.R. Carino,˜ T. Kent, D.H. Myers, C. Stacy, M. Sylvanus, A.L. Turner, K. Watanabe, and W.T. Ziemba. The Russel-Yasuda-Kasai model: An asset-liability model for a Japanese insurance company using multistage stochastic programming. Interfaces, 24(1):29–49, 1994. [563] C.C. Carøe, A. Ruszczynski,´ and R. Schultz. Unit commitment under uncertainty via two-stage stochastic programming. Technical Report DIKU-TR-97/23, Department of Computer Science, University of Copenhagen, 1997. [564] C.C. Carøe and J. Tind. A cutting-plane approach to mixed 0 − 1 stochastic integer programs. European Journal of Operational Research, 101(2):306–316, 1997. [565] Claus C. Carøe. Decomposition in stochastic integer programming. Ph.d. thesis, University of Copenhagen, Denmark, 1998. [566] Claus C. Carøe and Rudiger¨ Schultz. Dual decomposition in stochastic integer programming. Oper. Res. Lett., 24(1-2):37–45, 1999. [567] Claus C. Carøe and Jørgen Tind. L-shaped decomposition of two-stage stochastic programs with integer recourse. Math. Programming, 83(3, Ser. A):451–464, 1998. [568] Richard J. Caron, Arnon Boneh, and Shahar Boneh. Redundancy. In Advances in sensitivity analysis and parametric programming, pages 13.1–13.41. Kluwer Acad. Publ., Boston, MA, 1997. [569] R.J. Caron, M. Hlynka, and J.F. McDonald. On the best case performance of hit and run methods for detecting necessary constraints. Math. Programming, 54(2, Ser. A):233–249, 1992. [570] P. Carpentier, G. Cohen, and J.-C. Culioli. Stochastic optimal control and decomposition- coordination methods — part i: Theory. In: Recent Developments in Optimization, Roland Durier and Christian Michelot (Eds.), LNEMS 429:72–87, Springer-Verlag, Berlin, 1995. [571] P. Carpentier, G. Cohen, and J.-C. Culioli. Stochastic optimal control and decomposition- coordination methods — part ii: Application. In: Recent Developments in Optimization, Roland Durier and Christian Michelot (Eds.), LNEMS 429:88–103, Springer-Verlag, Berlin, 1995. [572] P. Carpentier, G. Cohen, J.-C. Culioli, and A. Renaud. Stochastic optimization of unit commitment: a new decomposition framework. IEEE Transactions on Power Systems 11(2):1067–1073, 1996. [573] Robert L. Carraway, Thomas L. Morin, and Herbert Moskowitz. Generalized dynamic programming for stochastic combinatorial optimization. Oper. Res., 37(5):819–829, 1989. [574] Robert L. Carraway, Robert L. Schmidt, and Lawrence R. Weatherford. An algorithm for maximizing target achievement in the stochastic knapsack problem with normal returns. Naval Res. Logist., 40(2):161–173, 1993. [575] E. Carrizosa, M. Munoz-M˜ arquez,´ and J. Puerto. Optimal positioning of a mobile service unit on a line. Ann. Oper. Res., 111:75–88, 2002. Recent developments in the theory and applications of location models, Part II. [576] Gh. Cartianu and Edmond Nicolau, editors. Prelucrarea s¸i transmiterea numerica a datelor s¸i con- ducerea proceselor cu ajutorul calculatoarelor, volume 10 of Probleme de Automatizare [Problems of Automation]. Editura Academiei Republicii Socialiste Romania,ˆ Bucharest, 1978. [577] D. Carton. Programmes lineaires´ stochastiques. Bull. Direction Etudes´ Recherches Ser.´ C Math. Informat., 1(3):43–60, 1968. [578] A. Casado and R. Blanco. A method for transforming stochastic nonlinear programming problems into deterministic ones for a class T of functions. Investigacion´ Oper., 7(2):3–9, 1986. [579] A. Casado and J. Ru´iz. On a stochastic quadratic programming problem. Investigacion´ Oper., 5(1):3–11, 1984.

33 [580] Michael S. Casey and Suvrajeet Sen. The scenario generation algorithm for multistage stochastic linear programming. Math. Oper. Res., 30(3):615–631, 2005. [581] R.G. Cassidy, C.A. Field, and M.J.L. Kirby. Two stage programming under uncertainty: a game theoretic approach. Cahiers Centre Etud. Rech. oper. 15, 39-55, 1973. [582] David A. Castanon˜ and Z. Bo Tang. A counterexample to: “Adaptive partitioned random search to global optimization” [IEEE Trans. Automat. Control 39 (1994), no. 11, 2235–2244; MR 95m:90123] by Tang. IEEE Trans. Automat. Control, 41(2):310, 1996. [583] J. Casti. Forest monitoring and harvesting policies. Appl. Math. Comput. 12, 19-48, 1983. [584] Zdenekˇ Castorˇ al.´ Stochastic nonlinear learning systems. Information Processing Machines, 18:233–262, 1975. [585] Olivier Catoni. The energy transformation method for the Metropolis algorithm compared with simulated annealing. Probab. Theory Related Fields, 110(1):69–89, 1998. [586] Douglas W. Caves and Joseph A. Herriges. Optimal dispatch of interruptible and curtailable service options. Oper. Res. 40, No.1, 104-112, 1992. [587] Yair Censor, Alvaro R. De Pierro, and Alfredo N. Iusem. Optimization of Burg’s entropy over linear constraints. Appl. Numer. Math., 7(2):151–165, 1991. [588] Yair Censor and Arnold Lent. Optimization of “log x” entropy over linear equality constraints. SIAM J. Control Optim., 25(4):921–933, 1987. [589] Yair Censor and Stavros A. Zenios. Parallel Optimization: Theory, Algorithms and Applications. Oxford University Press, Oxford, UK, 1997. [590] I.P. Cernopiskii.ˇ Remarks on the existence of a saddle point in stochastic programming problems. In Mathematical methods for the study and optimization of systems (Proc. Sem. Theory of Optimal Decisions, Kiev, 1970) (Russian), pages 221–224, Kiev., 1971. Akad. Nauk Ukrain. SSR Inst. Kibernet. [591] Cristiano Cervellera, Aihong Wen, and Victoria C. P. Chen. Neural network and regression spline value function approximations for stochastic dynamic programming. Comput. Oper. Res., 34(1):70–90, 2007. [592] Debjani Chakraborty. Redeﬁning chance-constrained programming in fuzzy environment. Fuzzy Sets and Systems, 125(3):327–333, 2002. Theme: decision and optimization. [593] T.K. Chakraborty. Stochastic parameter single sampling plans of given strength. Bull., Calcutta Stat. Assoc. 41, No.161-164, 117-126, 1991. [594] T.K. Chakraborty. Single sampling LTPD plans as a stochastic programming problem. Sankhya¯ Ser. B, 54(2):242–248, 1992. [595] Raymond H. Chan and Wai Ki Ching. A direct method for stochastic automata networks. In Applied probability (Hong Kong, 1999), volume 26 of AMS/IP Stud. Adv. Math., pages 1–15. Amer. Math. Soc., Providence, RI, 2002. [596] T. M. Chan. Geometric applications of a randomized optimization technique. Discrete Comput. Geom., 22(4):547–567, 1999. 14th Annual ACM Symposium on Computational Geometry (Min- neapolis, MN, 1998). [597] Suresh Chandra and T.R. Gulati. A duality theorem for a nondifferentiable fractional programming problem. Management Sci., 23(1):32–37, 1975/76.

34 [598] C.B. Chang and L.C. Youens. Measurement correlation for multiple sensor tracking in a dense target environment. IEEE Trans. Autom. Control AC-27, 1250-1252, 1982. [599] H. S. Chang. On the probability of correct selection by distributed voting in the stochastic optimization. J. Optim. Theory Appl., 125(1):231–240, 2005. [600] Hyeong Soo Chang. Multi-policy improvement in stochastic optimization with forward recursive function criteria. J. Math. Anal. Appl., 305(1):130–139, 2005. [601] Hyeong Soo Chang, Michael C. Fu, Jiaqiao Hu, and Steven I. Marcus. An asymptotically efficient simulation-based algorithm for finite horizon stochastic dynamic programming. IEEE Trans. Automat. Control, 52(1):89–94, 2007. [602] Ryong Sop Chang. An algorithm for stochastic extremum problems with upper-half gradient. Cho- son In-min Kong-hwa-kuk Kwa-hak-won T’ong-bo, 5:10–15, 1983. [603] Ryong Sop Chang. An algorithm of the modified stochastic conjugate gradient method and its convergence. Cho-son In-min Kong-hwa-kuk Kwa-hak-won T’ong-bo, 2:18–22, 1984. [604] Shih Sen Chang and Nan Jing Huang. Generalized random multivalued quasi-complementarity problems. Indian J. Math., 35(3):305–320, 1993. [605] Pavel Charamza. Comparison of the stochastic approximation software. In Computational aspects of model choice (Prague, 1991), Contrib. Statist., pages 163–176. Physica, Heidelberg, 1993. [606] Moses Charikar, Chandra Chekuri, and Martin Pal.´ Sampling bounds for stochastic optimization. In Approximation, randomization and combinatorial optimization, volume 3624 of Lecture Notes in Comput. Sci., pages 257–269. Springer, Berlin, 2005. [607] V. Charles and D. Dutta. A method for solving linear stochastic fractional programming problem with mixed constraints. Acta Cienc. Indica Math., 30(3):497–506, 2004. [608] V. Charles and D. Dutta. Linear stochastic fractional programming with sum-of-probabilistic- fractional objective. Optimization Online, http://www.optimization-online.org, 2005. [609] V. Charles and D. Dutta. Non-linear stochastic fractional programming models of financial derivatives. Optimization Online, http://www.optimization-online.org, 2005. [610] A. Charnes, Y.C. Chang, and J. Semple. Semi-infinite relaxation of joint chance constraints in chance-constrained programming. I. Zero-order stochastic decision rules. Internat. J. Systems Sci., 23(7):1051–1061, 1992. [611] A. Charnes and W.W. Cooper. A comment on Blau’s dilemma in stochastic programming and Bayesian decision analysis. Management Sci., 22(4):498–500, 1975/76. [612] A. Charnes, W.W. Cooper, and M.J.L. Kirby. Chance-constrained programming: an extension of statistical method. In Optimizing methods in statistics (Proc. Sympos., Ohio State Univ., Columbus, Ohio, 1971), pages 391–402, New York, 1971. Academic Press. [613] A. Charnes, W.W. Cooper, D. Klingman, and R.J. Niehaus. Explicit solutions in convex goal programming. Management Sci. 2 438-448 (1976)., 1975. [614] A. Charnes, W.W. Cooper, and G.H. Symonds. Cost horizons and certainty equivalents: An approach to stochastic programming of heating oil. Management Science, 4:183–195, 1958. [615] A. Charnes, Fred Glover, and D. Klingman. The lower bounded and partial upper bounded distribution model. Naval. Res. Logist. Quart. 18, 277-281, 1971.

35 [616] A. Charnes and M. Kirby. Optimal decision rules for the triangular E-model of chance-constrained programming. Cah. Cent. Etud. Rech. Oper. 11, 215-243, 1969. [617] A. Charnes, M.J.L. Kirby, and W.M. Raike. An acceptance region theory for chance-constrained programming. J. Math. Anal. Appl. 32, 38-61, 1970. [618] Abraham Charnes, Kingsley E. Haynes, Jared E. Hazleton, and Michael J. Ryan. An hierarchical goal programming approach to environmental-land use management. In Math. Anal. Decis. Probl. Ecol., Proc. NATO Conf., Istanbul 1973, Lect. Notes Biomath. 5, 2-13, 1975. [619] Bernard Chazelle. Deterministic sampling and optimization. In System modelling and optimization (Compiegne,` 1993), volume 197 of Lecture Notes in Control and Inform. Sci., pages 42–54. Springer, London, 1994. [620] Baoqian Chen. The convergence of a random search algorithm for unconstrained optimization problems. Math. Numer. Sin. 6, 166-173, 1984. [621] Han-Fu Chen. Optimization based on information containing uncertainties. Kybernetes, 30(9- 10):1177–1182, 2001. [622] Han-Fu Chen. Stochastic approximation and its applications, volume 64 of Nonconvex Optimiza- tion and its Applications. Kluwer Academic Publishers, Dordrecht, 2002. [623] Han-Fu Chen and Hai-Tao Fang. Nonconvex stochastic optimization for model reduction. J. Global Optim., 23(3-4):359–372, 2002. Nonconvex optimization in control. [624] Hanfu Chen. Stochastic approximation algorithm randomly truncated at time-varying bounds. Annu. Rev. Autom. Program. 12, part 1, 380-383, 1985. [625] Hanfu Chen. Stochastic approximation with state-dependent noise. Sci. China Ser. E, 43(5):531– 541, 2000. [626] Hanfu Chen and Lei Guo. Stochastic adaptive pole-zero assignment with convergence analysis. Syst. Control Lett. 7, 159-164, 1986. [627] Hanfu Chen and Qian Wang. Continuous-time Kiefer-Wolfowitz algorithm with randomized differences. Systems Sci. Math. Sci., 11(4):327–341, 1998. [628] H.F. Chen and P.E. Caines. The strong consistency of the stochastic gradient algorithm of adaptive control. IEEE Trans. Autom. Control AC-30, 189-192, 1985. [629] H.F. Chen, T.E. Duncan, and B. Pasik-Duncan. A stochastic approximation algorithm with random differences. In Proceedings of the 13th IFAC World Congress, volume H, pages 493–496, 1996. [630] Hong Chen, Ping Yang, David D. Yao, and Xiuli Chao. Optimal control of a simple assembly system. Oper. Res. Lett., 14(4):199–205, 1993. [631] Michael Chen and Sanjay Mehrotra. Self-concordant tree and decomposition based interior point methods for stochastic convex optimization problem. Stochastic Programming E-Print Series, http://www.speps.org, 2007. [632] Patrick S. Chen. On the minimum solution of the inventory system for deteriorating items with shortages and time-varying demand. J. Inform. Optim. Sci., 22(2):283–295, 2001. [633] Shao Zhong Chen and Zuo Shu Liu. Random ﬁxed-point theorems in abstract spaces. Acta Math. Sci., 1(2):133–144, 1981. [634] Shenghui Chen and Qinghua Chen. A weighted network model based on the preferential selection of edges. Appl. Math. Sci. (Hikari), 1(21-24):1145–1156, 2007.

36 [635] Shih-Pin Chen. An alternating variable method with varying replications for simulation response optimization. Comput. Math. Appl., 48(5-6):769–778, 2004. [636] Victoria C. P. Chen. Measuring the goodness of orthogonal array discretizations for stochastic programming and stochastic dynamic programming. SIAM J. Optim., 12(2):322–344 (electronic), 2001/02. [637] X. Chen. Newton-type methods for stochastic programming. Math. Comput. Modelling, 31(10- 12):89–98, 2000. Stochastic models in engineering, technology, and management (Gold Coast, 1996). [638] Xiao Jun Chen, Li Qun Qi, and Robert S. Womersley. Newton’s method for quadratic stochastic programs with recourse. J. Comput. Appl. Math., 60(1-2):29–46, 1995. Linear/nonlinear iterative methods and veriﬁcation of solution (Matsuyama, 1993). [639] Xiaojun Chen and Robert S. Womersley. A parallel inexact Newton method for stochastic programs with recourse. Ann. Oper. Res., 64:113–141, 1996. Stochastic programming, algorithms and models (Lillehammer, 1994). [640] Z. L. Chen and W. B. Powell. Convergent cutting-plane and partial-sampling algorithm for multistage stochastic linear programs with recourse. J. Optim. Theory Appl., 102(3):497–524, 1999. [641] Zeng Jing Chen. Stochastic programming problems in securities markets. Qufu Shifan Daxue Xuebao Ziran Kexue Ban, 21(5):172–177, 1995. [642] Zeng Jing Chen. Stochastic programming problems in securities markets. Shandong Daxue Xuebao Ziran Kexue Ban, 31(1):42–47, 1996. [643] Zhi-Long Chen, Shanling Li, and Devanath Tirupati. A scenario-based stochastic programming approach for technology and capacity planning. Comput. Oper. Res., 29(7):781–806, 2002. [644] Zhi Ping Chen and Yong Gao. Stationary and Markov properties of optimal solution processes for stochastic programming problems with random processes. Pure Appl. Math., 12(1):88–92, 1996. [645] Zhi Ping Chen and Yong Gao. Process properties and stability of optimal solution sets of stochastic programming problems with random processes. Acta Math. Appl. Sinica, 20(3):466–472, 1997. [646] Zhi Ping Chen and Cheng Xian Xu. Generalized duality theory for general multistage programming problems with recourse. J. Math. Res. Exposition, 17(2):275–286, 1997. [647] Zhiping Chen. On the convergence of sampling algorithms for solving dynamic stochastic programming. Systems Sci. Math. Sci., 13(4):397–406, 2000. [648] Zhiping Chen and Chengxian Xu. A dual gradient method for solving a class of two-stage com- pensating problems. Math. Appl., 9(3):266–271, 1996. [649] Zhiping Chen and Chengxian Xu. Global convergence of a general sampling algorithm for dynamic nonlinear stochastic programs. Numer. Funct. Anal. Optim., 23(5-6):495–514, 2002. [650] T.C.E. Cheng. Capacity requirements planning by stochastic linear programming. Math. Modelling 7, 443-448, 1986. [651] A.G. Chentsov. On the correct extension of some problems with stochastic constraints. Avtomat. i Telemekh., 7:68–79, 1995. [652] Myun-Seok Cheon, Shabbir Ahmed, and Faiz Al-Khayyal. A branch-reduce-cut algorithm for the global optimization of probabilistically constrained linear programs. Stochastic Programming E-Print Series, http://www.speps.org, 2005.

37 [653] Myun-Seok Cheon, Shabbir Ahmed, and Faiz Al-Khayyal. A branch-reduced-cut algorithm for the global optimization of probabilistically constrained linear programs. Math. Program., 108(2-3, Ser. B):617–634, 2006. [654] Raymond K.-M. Cheung and Warren B. Powell. SHAPE—a stochastic hybrid approximation procedure for two-stage stochastic programs. Oper. Res., 48(1):73–79, 2000. [655] Raymond K.-M. Cheung and Warren B. Powell. SHAPE—a stochastic hybrid approximation procedure for two-stage stochastic programs. Oper. Res., 48(1):73–79, 2000. [656] Tran Quoc Chien. Semistochastic decomposition scheme in mathematical programming and game theory. Kybernetika (Prague), 27(6):535–541, 1991. [657] A. Chikan and I. Dobos. A concept of uncertainty and risk. PU.M.A., Pure Math. Appl., Ser. C 2, No.1, 87-94, 1991. [658] J.B. Chilton. Maximum principle for the optimal control of systems with continuous leads. J. Optim. Theory Appl., 69(2):343–350, 1991. [659] D.C. Chin. A more efficient global optimization algorithm based on Styblinski and Tang. Neural Networks, 7:573–574, 1994. [660] D.C. Chin. Efficient identification procedure for inversion processing. In Proceedings of the IEEE Conference on Decision and Control, pages 3129–3130, 1996. [661] D.C. Chin. Comparative study of stochastic algorithms for system optimization based on gradient approximations. IEEE Transactions on Systems, Man, and Cybernetics B, 27:244–249, 1997. [662] D.C. Chin. The simultaneous perturbation method for processing magnetospheric images. Optical Engineering, 38:606–611, 1999. [663] D.C. Chin and R.H. Smith. A traffic simulation for mid-Manhattan with model-free adaptive signal control. In Proceedings of the Summer Computer Simulation Conference, pages 296–301, 1994. [664] D.C. Chin and R. Srinivasan. Electrical conductivity object locator: location of small objects buried at shallow depths. In Proceedings of the Unexploded Ordnance (UXO) Conference, pages 50–57, 1997. [665] Anukal Chiralaksanakul and David P. Morton. Assessing policy quality in multi-stage stochastic programming. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [666] Gyeong-Mi Cho. Stability analysis of two-stage stochastic programming problems. Bull. Korean Math. Soc., 31(2):243–252, 1994. [667] Gyeong-Mi Cho. Stability of the multiple objective linear stochastic programming problems. Bull. Korean Math. Soc., 32(2):287–296, 1995. [668] Gyeong-Mi Cho. Stability in two-stage multiobjective stochastic programming. Nonlinear Anal., 47(6):3641–3648, 2001. Proceedings of the Third World Congress of Nonlinear Analysts, Part 6 (Catania, 2000). [669] Gyeong-Mi Cho. Log-barrier method for two-stage quadratic stochastic programming. Appl. Math. Comput., 164(1):45–69, 2005. [670] Michal Chobot. A stochastic approach to goal programming. Ekonom.-Mat. Obzor, 9:305–319, 1973. [671] Milan Chobot. Goal-interval programming, and a stochastic approach to decentralization problems. In Second National Conference on Mathematical Methods in Economics (Harmonia,´ 1972) (Czech), pages 69–93. Ekonom.-Mat. Lab. Ekonom. Ustavu´ Ceskoslov.ˇ Akad. Ved,ˇ Prague, 1973.

38 [672] Christine Choirat, Christian Hess, and Raffaello Seri. Approximation of stochastic programming problems. In Monte Carlo and quasi-Monte Carlo methods 2004, pages 45–59. Springer, Berlin, 2006. [673] Tahir Choulli, Michael Taksar, and Xun Yu Zhou. Excess-of-loss reinsurance for a company with debt liability and constraints on risk reduction. Quant. Finance, 1(6):573–596, 2001. [674] Tahir Choulli, Michael Taksar, and Xun Yu Zhou. Excess-of-loss reinsurance for a company with debt liability and constraints on risk reduction. Quant. Finance, 1(6):573–596, 2001. [675] Chee-Seng Chow and John N. Tsitsiklis. The complexity of dynamic programming. J. Complexity 5, No.4, 466-488, 1989. [676] Yunshyong Chow and June Hsieh. On occupation times of annealing processes. Bull. Inst. Math. Acad. Sinica, 20(1):19–26, 1992. [677] Anthony H. Christer, Shunji Osaki, and Lyn C. Thomas, editors. Stochastic modelling in innovative manufacturing, volume 445 of Lecture Notes in Economics and Mathematical Systems. Springer- Verlag, Berlin, 1997. Papers from the UK-Japanese Workshop held at Churchill College, University of Cambridge, Cambridge, July 21–22, 1995. [678] D. Christiansen and S.W. Wallace. Option theory and modeling under uncertainty. In E. Matson, A. Tomasgard, E. Meistad and S. Dye (eds.), Essays in honour of Bjorn Nygreen on his 50th Birthday, Dept. of Man. Econ. and OR, Norwegian Univ. of Sc. and Technology, Trondheim, 147-168, 1996. [679] H.Dalgas Christiansen. Monte Carlo optimization in K-space. - Global and path approach. In Proc. Stat. Comput. Sect., Annu. Meet. Am. Stat. Assoc., Cincinnati/Ohio 1982, 200-205, 1982. [680] Piotr Chrzan. An application of sample distributions for seeking the ”optimal” solution for probabilistic programming problems. Przegl. Stat. 28, 29-38, 1981. [681] Piotr Chrzan. Application of the Chebyshev inequality for determining deterministic equivalents of probabilistic models. Przeglk ad Statyst., 28(3-4):247–254 (1982), 1981. [682] S.N. Chuang, T.T. Soong, and K.H. Chen. Stochastic extensions to necessary conditions in the theory of the calculus of variations. J. Optimization Theory Appl., 23(1):53–64, 1977. [683] Chia-Shin Chung and James Flynn. Optimal replacement policies for k-out-of-n systems. IEEE Trans. Reliab. R-38, No.4, 462-467, 1989. [684] S.L. Chung, F.B. Hanson, and H.H. Xu. Parallel stochastic dynamic programming: ﬁnite element methods. Linear Algebra Appl., 172:197–218, 1992. Second NIU Conference on Linear Algebra, Numerical Linear Algebra and Applications (DeKalb, IL, 1991). [685] Olga R. Chuyan and Aleksei G. Sukharev. On adaptive and nonadaptive stochastic and deterministic algorithms. J. Complexity, 6(1):119–127, 1990. [686] T. Cipra. Gaussian processes in linear programs with random right-hand sides. Z. Angew. Math. Mech., 68(5):T438–T439, 1988. [687] Toma´sˇ Cipra. Moment problem with given covariance structure in stochastic programming. Ekonom.-Mat. Obzor, 21(1):66–77, 1985. [688] Toma´sˇ Cipra. Prediction in stochastic linear programming. Kybernetika (Prague), 23(3):214–226, 1987. [689] Toma´sˇ Cipra. Autoregressive processes in optimization. J. Appl. Probab., 25(2):302–312, 1988. [690] Toma´sˇ Cipra. Stochastic programming with random processes. Ann. Oper. Res., 30(1-4):95–105, 1991. Stochastic programming, Part I (Ann Arbor, MI, 1989).

39 [691] Toma´sˇ Cipra and Jitka Dupacovˇ a.´ Selected applications of stochastic programming and a survey of software. Ekonom.-Mat. Obzor, 22(3):241–262, 1986. [692] A.M. Cirlin. Optimierung im Mittel und gleitende Regimes in Problemen der optimalen Regelung. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1974, Nr. 2, 143-151, 1974. [693] Steven P. Clark and Peter C. Kiessler. On the convexity of value functions for a certain class of stochastic dynamic programming problem. Stochastic Anal. Appl., 20(4):783–789, 2002. [694] Hans Joachim Cleef. Loesungsverfahren fuer eine Klasse zweistufiger stochastischer Opti- mierungsprobleme. Mathematisch-Naturwissenschaftliche Fakultaet der Rheinischen Friedrich- Wilhelms-Universitaet zu Bonn. 80 S., 1980. [695] H.J. Cleef. A solution procedure for the two-stage stochastic program with simple recourse. Z. Oper. Res. Ser. A-B, 25(1):A1–A13, 1981. [696] H.J. Cleef and W. Gaul. A stochastic flow problem. J. Inf. Optimization Sci. 1, 229-270, 1980. [697] H.J. Cleef and W. Gaul. Project scheduling via stochastic programming. Math. Operationsforsch. Statist. Ser. Optim., 13(3):449–468, 1982. [698] Moise Cocan. Ueber die Bellmansche Funktionalgleichung fuer stochastische dynamische Prozesse. (On the Bellman functional equation for stochastic dynamic processes). Bul. Univ. Brasov, Ser. C 31, 13-18, 1989. [699] Moise Cocan. The model of a stochastic dynamic programming problem in case of processes with an infinite number of periods. Bul. Univ. Bras¸ov Ser. C, 32:55–61, 1990. [700] Ju.M. Codikov and A.S. Hohlov. Extrapolation fuer innere Penaltyfunktionen. Izv. Akad. Nauk SSSR, Tekh. Kibernet. 1977, No.2, 32-38, 1977. [701] E. G. Coffman, Jr., George S. Lueker, Joel Spencer, and Peter M. Winkler. Packing random rectangles. Probab. Theory Related Fields, 120(4):585–599, 2001. [702] Jr. Coffman, E.G., D.S. Johnson, P.W. Shor, and G.S. Lueker. Probabilistic analysis of packing and related partitioning problems. In Probability and algorithms, pages 87–107. Nat. Acad. Press, Washington, DC, 1992. [703] G. Cohen. Information exchange between independent stochastic systems. Journal of Optimization Theory and Applications 32(2), 1980. [704] G. Cohen and P. Bernhard. On the rationality of some decision rules in a stochastic environment. IEEE Transactions on Automatic Control, AC-24, Nr. 5, 1979. [705] G. Cohen and J.-C. Culioli. Decomposition and coordination in stochastic optimization. 4th IFAC Symposium on Large Scale Systems Theory and Applications, Zurich, 1986. [706] Guy Cohen and Jean-Christophe Culioli. Algorithmes de decomposition/coordination´ en optimisation stochastique. RAIRO Automat.-Prod. Inform. Ind., 20(3):253–272, 1986. [707] Ch. Condevaux-Lanloy, E. Fragniere, and A.J. King. SISP, simplified interface for stochastic programming establishing a hard link between mathematical programming modeling languages and SMPS codes. Optimization Methods and Software, 17(3):423–443, 2002. [708] Christian Condevaux-Lanloy, Emmanuel Fragniere,` and Alan J. King. SISP: simplified interface for stochastic programming: establishing a hard link between mathematical programming modeling languages and SMPS codes. Optim. Methods Softw., 17(3):423–443, 2002. Stochastic programming. [709] E. Contini. A stochastic approach to goal programming. Oper. Res. 16, 576-586, 1968.

40 [710] W.D. Cook, M.J.L. Kirby, and S.L. Mehndiratta. A structured nonlinear programming problem. Rev. Belg. Stat. Inf. Rech. Oper. 17, No.4, 43-55, 1977. [711] R. Cooke and J.D. Pinter. Optimization in risk management. Civil Engineering Systems, 6:122– 128, 1989. [712] Leon Cooper. The stochastic transportation-location problem. Comput. Math. Appl., 4(3):265–275, 1978. [713] William W. Cooper, H. Deng, Zhimin Huang, and Susan X. Li. Chance constrained programming approaches to congestion in stochastic data envelopment analysis. European J. Oper. Res., 155(2):487–501, 2004. [714] W.W. Cooper, Zhimin Huang, and Susan X. Li. Satisﬁcing DEA models under chance constraints. Ann. Oper. Res., 66:279–295, 1996. Extensions and new developments in data envelopment analysis. [715] Don Coppersmith and Gregory B. Sorkin. Constructive bounds and exact expectations for the random assignment problem. Random Structures Algorithms, 15(2):113–144, 1999. [716] A. Corana, M. Marchesi, C. Martini, and S. Ridella. Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm. ACM Trans. Math. Software 13, 262-280, 1987. [717] Adrian Corban. The stochastic threedimensional transportation problem. Stud. Cercet. Mat. 24, 513-517, 1972. [718] Adrian Corban. Linear tridimensional programming. Revue Roumaine Math. pur. appl. 20, 897- 905, 1975. [719] K. Cormican, D.P. Morton, and R.K. Wood. Stochastic network interdiction. Operations Research, 46:184–197, 1998. [720] Andrea Corradini, Ugo Montanari, Francesca Rossi, Hartmut Ehrig, and Michael Loewe. Graph grammars and logic programming. In Graph grammars and their application to computer science, Proc. 4th Int. Workshop, Bremen/Ger. 1990, Lect. Notes Comput. Sci. 532, 221-237, 1991. [721] Andre Costa. Ants, stochastic optimisation and reinforcement learning. Austral. Math. Soc. Gaz., 32(2):116–123, 2005. [722] A.M. Couhault. Quelques methodes de resolution d’un probleme de programmation stochastique lineaire venant de la gestion des stocks. IRIA, Cahier Nr. 9, 77-100, 1972. [723] A.B. Cox and Jr. Bryson, A.E. Identiﬁcation by a combined smoothing nonlinear programming algorithm. Automatica—J. IFAC, 16(6):689–694, 1980. [724] Dennis D. Cox and Susan John. SDO: a statistical method for global optimization. In Multidisci- plinary design optimization (Hampton, VA, 1995), pages 315–329. SIAM, Philadelphia, PA, 1997. [725] Louis Anthony Cox, Jr. and Djangir A. Babayev. Optimization under uncertainty via random sampling of scenarios. I. Appl. Comput. Math., 3(2):95–106, 2004. [726] M. L. A. G. Cremers, W. K. Klein Haneveld, and M. H. van der Vlerk. A two-stage model for a day-ahead paratransit planning problem. In CTW2006—Cologne-Twente Workshop on Graphs and Combinatorial Optimization, volume 25 of Electron. Notes Discrete Math., page 35 (electronic). Elsevier, Amsterdam, 2006. [727] Allan B. Cruse. Some combinatorial properties of centrosymmetric matrices. Linear Algebra and Appl., 16(1):65–77, 1977.

41 [728] Janos Csirik. Bin packing as a random walk: A note on Knoedel’s paper. Oper. Res. Lett. 5, 161-163, 1986. [729] M. Cugiani. Some stochastic strategies in optimization problems. In Variational inequalities and complementarity problems, theory and applications, Proc. int. School Math., Erice/Sicily 1978, 105-126, 1980. [730] Di Cui, Xiang Bin Sun, and Wei Zhang. Stochastic programming with an improved Wolef-BFGS- SQP method. J. Shandong Univ. Sci. Technol. Nat. Sci., 24(2):94–96, 2005. [731] J.-C. Culioli and G. Cohen. Decomposition/coordination algorithms in stochastic optimization. SIAM J. Control Optim., 28(6):1372–1403, 1990. [732] J.-C. Culioli and G. Cohen. Optimisation stochastique sous contraintes en esperance.´ Comptes Rendus de l’Academie´ des Sciences, Paris, t.320, Serie´ I, 735–758, 1995. [733] A.A. Cunningham and D.M. Frances. A data collection strategy for estimation of cost coefﬁcients of a linear programming model. Management Sci. 22, 1074-1080, 1976. [734] V.I. Curkov. The two-stage stochastic programming problem of block type. Z.ˇ Vycisl.ˇ Mat. i Mat. Fiz., 18(2):360–369, 524, 1978. [735] Jaksaˇ Cvitanic´ and Ioannis Karatzas. Convex duality in constrained portfolio optimization. Ann. Appl. Probab., 2(4):767–818, 1992. [736] Ja.Z. Cypkin, A.I. Kaplinskii, and A.S. Krasnenker. Methoden der lokalen Verbesserung in Prob- lemen der stochastischen Optimierung. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1973, Nr. 6, 3-11, 1973. [737] N.D. Dagkesamanskii. A stochastic problem of optimization of multimode installations. In Ques- tions of mathematical cybernetics and applied mathematics, No. 3 (Russian), pages 93–101. “Elm”,` Baku, 1978. [738] Roy W. Dahl, Karen Keating, Laurence Levy, Daryl J. Salamone, Barindra Nag, and Joan A. San- born. Weighted Hamiltonian augmentation method involving insertions. J. Guid. Control Dyn. 11, No.5, 412-414, 1988. [739] L. Dai, C. H. Chen, and J. R. Birge. Convergence properties of two-stage stochastic programming. J. Optim. Theory Appl., 106(3):489–509, 2000. [740] Fred´ eric´ Dambreville and Jean-Pierre Le Cadre. Detection of a Markovian target with optimization of the search efforts under generalized linear constraints. Naval Res. Logist., 49(2):117–142, 2002. [741] A.R. Danilin. Regularization of a control problem under conditions of uncertainty. In Some questions of operator theory, Collect. sci. Works, Sverdlovsk 1987, 20-28, 1987. [742] G. Dantzig and G. Infanger. Approaches to stochastic programming with application to electric power systems. In K. Frauendorfer, H. Glavitsch, and R. Bacher, editors, Optimization in Planning and Operation of Electric Power Systems, pages 125–138. Physica-Verlag, Heidelberg, 1993. [743] G. B. Dantzig. Decomposition techniques for large-scale electric power systems planning under uncertainty. In R. Sharda, B. L. Golden, E. Wasil, O. Balci, and W. Steward, editors, Impacts of Recent Computer Advances on Operations Research, pages 3–20. North-Holland, 1989. [744] G. B. Dantzig and G. Infanger. Intelligent control and optimization under uncertainty with application to hydro power. European Journal of Operational Research, 97(2):396–407, 1997. [745] G.B. Dantzig. Linear programming under uncertainty. Management Science, 1:197–206, 1955.

42 [746] G.B. Dantzig, M.A.H. Dempster, and M. Kallio, editors. Large Scale Linear Programming, Vols. 1 and 2. IIASA, Laxenburg, 1981. [747] George B. Dantzig. A generalized programming solution to a convex programming problem with a homogeneous objective. Research Report RR-73-21, IIASA - International Institute for Applied Systems Analysis, Laxenburg, Austria, 1973. [748] George B. Dantzig. Need to do planning under uncertainty and the possibility of using parallel processors for this purpose. Ekonom.-Mat. Obzor, 23(2):121–135, 1987. [749] George B. Dantzig and Peter W. Glynn. Parallel processors for planning under uncertainty. Ann. Oper. Res., 22(1-4):1–21, 1990. Supercomputers and large-scale optimization: algorithms, software, applications (Minneapolis, MN, 1988). [750] George B. Dantzig and Gerd Infanger. Large-scale stochastic linear programs—importance sampling and Benders decomposition. In Computational and applied mathematics, I (Dublin, 1991), pages 111–120. North-Holland, Amsterdam, 1992. [751] George B. Dantzig and Gerd Infanger. Multi-stage stochastic linear programs for portfolio optimization. Ann. Oper. Res., 45(1-4):59–76, 1993. [752] B. S. Darkhovskii. On an approach to the stochastic recovery problem. Avtomat. i Telemekh., (9):43–52, 2000. [753] M.S. Daskin. A maximum expected covering location model: formulation, properties and heuristic solution. Transportation Science, 17(1):48–70, 1983. [754] Gianfranco D’Atri. Outline of a probabilistic framework for combinatorial optimization. In Numer- ical techniques for stochastic systems (Conf., Gargnano, 1979), pages 347–368. North-Holland, Amsterdam, 1980. [755] Gianfranco D’Atri and Claude Puech. Probabilistic analysis of the subset-sum problem. Discrete Appl. Math. 4, 329-334, 1982. [756] K.J. Daun, J.R. Howell, and D.P. Morton. Geometric optimization of radiative enclosures containing specular surfaces, through non-linear programming. In International Mechanical Engineering Congress and Exposition, 2002. [757] K.J. Daun, J.R. Howell, and D.P. Morton. Geometric optimization of radiative enclosures containing specular surfaces. Journal of Heat Transfer, 125:845–851, 2003. [758] K.J. Daun, J.R. Howell, and D.P. Morton. Smoothing monte carlo exchange factors through constrained maximum likelihood estimation. Journal of Heat Transfer, 127:1124–1128, 2005. [759] H.T. David and Geung-Ho Kim. Pragmatic optimization of information functionals. In Optimizing methods in statistics, Proc. int. Conf., Bombay 1977, 167-181 , 1979. [760] M. Davidson. Primal-dual constraint aggregation with application to stochastic programming. Ann. Oper Res., 99:41–58 (2001), 2000. Applied mathematical programming and modeling, IV (Limas- sol, 1998). [761] M. R. Davidson and N. M. Novikova. The constraint aggregation method in a game-theoretic problem of stochastic programming. Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., 48(2):26– 29, 1998. [762] M. R. Davidson, N. M. Novikova, and D. D. Solomakhin. A method for searching for a stochastic saddle point with constraints satisﬁed almost surely. Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., (2):10–14, 48, 2000.

43 [763] M. R. Davidson and D. D. Solomakhin. A method for solving a stochastic programming problem with constraints satisfied almost surely. Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., 50(2):33–36, 1999. [764] M.H.A. Davis. Markov models and optimization, volume 49 of Monographs on Statistics and Applied Probability. Chapman & Hall, London, 1993. [765] M.H.A. Davis, M.A.H. Dempster, and R.J. Elliott. On the value of information in controlled diffusion processes. In Stochastic analysis, pages 125–138. Academic Press, Boston, MA, 1991. [766] G.V. Davydov and I.M. Davydova. Solubility of the system Ax = 0, x≥ 0 with indefinite coefficients. Sov. Math. 34, No.9, 108-112 translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1990, No.9(340), 85-88 (1990)., 1990. [767] R.van Dawen and M. Schael. On the existence of stationary optimal policies in Markov decision models. Z. Angew. Math. Mech. 63, T403-T404, 1983. [768] P.K. De, D. Acharya, and K.C. Sahu. A chance-constrained goal programming model for capital budgeting. J. Oper. Res. Soc. 33, 635-638, 1982. [769] Prabuddha De, Jay B. Ghosh, and Charles E. Wells. On the minimization of the weighted number of tardy jobs with random processing times and deadline. Comput. Oper. Res. 18, No.5, 457-463, 1991. [770] Prabuddha De, Jay B. Ghosh, and Charles E. Wells. On the solution of a stochastic bottleneck assignment problem and its variations. Nav. Res. Logist. 39, No.3, 389-397, 1992. [771] V. de Angelis. Minimax solution for linear programming problems under conditions of uncertainty. Metron, 34(1-2):101–121 (1978), 1976. [772] V.de Angelis. Linear programming with uncertain objective function: minimax solution for relative loss. Calcolo, 16(2):125–141, 1979. [773] V. de Angelis. Stochastic linear programming in the objective function: minimax solution for relative loss. In Proceedings of the First World Conference on Mathematics at the Service of Man (Barcelona, 1977), Vol. I, pages 248–271. Univ. Politec. Barcelona, 1980. [774] X. de Groote, M.-C. Noel,¨ and Y. Smeers. Some test problems for stochastic nonlinear multistage programs. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 515–541. Springer, Berlin, 1988. [775] W.J. De Lange and J.D. Pinter. Groundwater quality assessment and management: A stochastic modelling approach. Research Report 91.009, National Institute for Inland Water Management and Waste Water Treatment, Lelystad, 1991. [776] F. De Vylder. Bound on integrals: elimination of the dual and reduction of the number of equality constraints. Insurance Math. Econom., 2(3):139–145, 1983. [777] F. De Vylder. Maximization, under equality constraints, of a functional of a probability distribution. Insurance Math. Econom., 2(1):1–16, 1983. [778] I. Deak.´ Computation of multiple normal probabilities. In Recent results in stochastic programming (Proc. Meeting, Oberwolfach, 1979), volume 179 of Lecture Notes in Econom. and Math. Systems, pages 107–120, Berlin, 1980. Springer. [779] I. Deak.´ Three digit accurate multiple normal probabilities. Numer. Math., 35(4):369–380, 1980. [780] I. Deak.´ Computing probabilities of rectangles in case of multinormal distribution. J. Statist. Comput. Simulation, 26(1-2):101–114, 1986.

44 [781] I. Deak.´ Multidimensional integration and stochastic programming. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 187–200. Springer, Berlin, 1988. [782] Istvan´ Deak.´ Monte Carlo methods for computing probabilities of sets in higher-dimensional spaces in case of normal distribution. Alkalmaz. Mat. Lapok, 4(1-2):35–94 (1979), 1978. [783] Istvan´ Deak.´ Regression estimators related to multinormal distributions: computer experiences in root ﬁnding. In Stochastic programming methods and technical applications (Neubiberg/Munich, 1996), pages 279–293. Springer, Berlin, 1998. [784] Istvan´ Deak.´ Computing two-stage stochastic programming problems by successive regression approximations. In Stochastic optimization techniques (Neubiberg/Munich, 2000), volume 513 of Lecture Notes in Econom. and Math. Systems, pages 91–102. Springer, Berlin, 2002. [785] Istvan´ Deak.´ Solving stochastic programming problems by successive regression approximations— numerical results. In Dynamic stochastic optimization (Laxenburg, 2002), volume 532 of Lecture Notes in Econom. and Math. Systems, pages 209–224. Springer, Berlin, 2004. [786] Istvan´ Deak.´ Two-stage stochastic problems with correlated normal variables: computational experiences. Ann. Oper. Res., 142:79–97, 2006. [787] Brian C. Dean, Michel X. Goemans, and Jan Vondrak.´ Adaptivity and approximation for stochastic packing problems. In Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 395–404 (electronic), New York, 2005. ACM. [788] Morris H. DeGroot. Optimization with an uncertain objective. Stochastics, 21(2):97–112, 1987. [789] I. Dekany. Numerical solution of a stochastic control problem derived from Bensoussan-Lions. Inventory model. In Prog. Oper. Res., Eger 1974, Colloq. Math. Soc. Janos Bolyai 12, 231-242 , 1976. [790] P. Del Moral and G. Salut. Particle interpretation of nonlinear ﬁltering and optimization. Russian J. Math. Phys., 5(3):355–372 (1998), 1997. [791] Pierre Del Moral. Maslov optimization theory: topological aspects. In Idempotency (Bristol, 1994), pages 354–382. Cambridge Univ. Press, Cambridge, 1998. [792] Bernard Delyon and Anatoli Juditsky. Stochastic optimization with averaging of trajectories. Stochastics Stochastics Rep., 39(2-3):107–118, 1992. [793] Ron S. Dembo. Scenario optimization. Ann. Oper. Res., 30(1-4):63–80, 1991. Stochastic programming, Part I (Ann Arbor, MI, 1989). [794] Ron S. Dembo and Moshe Haviv. Truncated policy iteration methods. Oper. Res. Lett. 3, 243-246, 1984. [795] R.S. Dembo and A. King. Tracking models and the optimal regret distribution in asset allocation. Applied Stochastic Models and Data Analysis 8:151-157, 1992. [796] M. A. H. Dempster. Sequential importance sampling algorithms for dynamic stochastic programming. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 312(Teor. Predst. Din. Sist. Komb. i Algoritm. Metody. 11):94–129, 312–313, 2004. [797] M. A. H. Dempster, J. E. Scott, and G. W. P. Thompson. Stochastic modeling and optimization using STOCHASTICS. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 137–157. SIAM, Philadelphia, PA, 2005. [798] M.A.H. Dempster. On stochastic programming. I: Static linear programming under risk. J. math. Analysis Appl. 21, 304-343, 1968.

45 [799] M.A.H. Dempster. Introduction to stochastic programming. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 3–59. Academic Press, London, 1980. [800] M.A.H. Dempster, editor. Stochastic programming, London, 1980. Academic Press Inc. [Harcourt Brace Jovanovich Publishers]. The Institute of Mathematics and its Applications Conference Se- ries. [801] M.A.H. Dempster. A stochastic approach to hierarchical planning and scheduling. In Deterministic and stochastic scheduling (Durham, 1981), volume 84 of NATO Adv. Study Inst. Ser. C: Math. Phys. Sci., pages 271–296, Dordrecht, 1982. Reidel. [802] M.A.H. Dempster, editor. Proceedings of the IIASA Task Force Meeting in Stochastic Optimization. 1983. Stochastics 10, No. 3–4. [803] M.A.H. Dempster. On stochastic programming. II. Dynamic problems under risk. Stochastics, 25(1):15–42, 1988. [804] M.A.H. Dempster, M.L. Fisher, L. Jansen, B.J. Lageweg, J.K. Lenstra, and A.H.G. Rinnooy Kan. Analytical evaluation of hierarchical planning systems. Oper. Res. 29, 707-716, 1981. [805] M.A.H. Dempster, M.L. Fisher, L. Jansen, B.J. Lageweg, J.K. Lenstra, and A.H.G. Rinnooy Kan. Analysis of heuristics for stochastic programming: results for hierarchical scheduling problems. Math. Oper. Res., 8(4):525–537, 1983. [806] M.A.H. Dempster and A. Papagaki-Papoulias. Computational experience with an approximate method for the distribution problem. In Stochastic programming, Proc. int. Conf., Oxford 1974, 223-243, 1980. [807] Eric V. Denardo, Uriel G. Rothblum, and Arthur J. Swersey. A transportation problem in which costs depend on the order of arrival. Manage. Sci. 34, No.6, 774-783, 1988. [808] D. Dentcheva. Differentiable selections and Castaing representations of multifunctions. Mathe- matical Analysis and Applications, 223:371–396, 1998. [809] D. Dentcheva. Regular Castaing representations with application to stochastic programming. SIAM Journal on Optimization, 10:732–749, 2000. [810] D. Dentcheva, A. Prekopa, and A. Ruszczynski. On convex probabilistic programs with discrete distributions. Nonlinear Analysis: Theory, Methods & Applications, 47:1997–2009, 2001. [811] D. Dentcheva, A. Prekopa, and A. Ruszczynski. Bounds for integer stochastic programs with probabilistic constraints. Discrete Applied Mathematics, to appear. [812] D Dentcheva and W. Romisch.¨ Optimal power generation under uncertainty via stochastic programming. In K. Marti and P. Kall, editors, Stochastic Programming Methods and Technical Ap- plications, Lecture Notes in Economics and Mathematical Systems, volume 458, pages 22–56. Springer-Verlag, Berlin, 1998. [813] D. Dentcheva and A. Ruszczynski.´ Inverse stochastic dominance constraints and quantile utility theory. C. R. Acad. Bulgare Sci., 58(1):13–18, 2005. [814] Darinka Dentcheva. Regular Castaing representations of multifunctions with applications to stochastic programming. SIAM J. Optim., 10(3):732–749 (electronic), 2000. [815] Darinka Dentcheva. Approximations, expansions and univalued representations of multifunctions. Nonlinear Anal., 45(1, Ser. A: Theory Methods):85–108, 2001. [816] Darinka Dentcheva, Rene´ Henrion, and Andrzej Ruszczynski.´ Stability and sensitivity of optimization problems with ﬁrst order stochastic dominance constraints. SIAM J. Optim., 18(1):322–337 (electronic), 2007.

46 [817] Darinka Dentcheva, Bogumila Lai, and Andrzej Ruszczynski.´ Efficient point methods for probabilistic optimization problems. Stochastic Programming E-Print Series, http://www.speps. org, 2003. [818] Darinka Dentcheva, Bogumila Lai, and Andrzej Ruszczynski.´ Dual methods for probabilistic optimization problems. Math. Methods Oper. Res., 60(2):331–346, 2004. [819] Darinka Dentcheva, Andras´ Prekopa,´ and Andrzej Ruszczynski.´ Concavity and efficient points of discrete distributions in probabilistic programming. Math. Program., 89(1, Ser. A):55–77, 2000. [820] Darinka Dentcheva, Andras´ Prekopa,´ and Andrzej Ruszczynski.´ On convex probabilistic programming with discrete distributions. Nonlinear Anal., 47(3):1997–2009, 2001. Proceedings of the Third World Congress of Nonlinear Analysts, Part 3 (Catania, 2000). [821] Darinka Dentcheva, Andras´ Prekopa,´ and Andrzej Ruszczynski.´ Bounds for probabilistic integer programming problems. Discrete Appl. Math., 124(1-3):55–65, 2002. Workshop on Discrete Optimization (Piscataway, NJ, 1999). [822] Darinka Dentcheva and Werner Romisch.¨ Differential stability of two-stage stochastic programs. SIAM J. Optim., 11(1):87–112 (electronic), 2000. [823] Darinka Dentcheva and Werner Romisch.¨ Duality gaps in nonconvex stochastic optimization. Math. Program., 101(3, Ser. A):515–535, 2004. [824] Darinka Dentcheva, Werner Romisch,¨ and Rudiger¨ Schultz. Strong convexity and directional derivatives of marginal values in two-stage stochastic programming. In Stochastic programming (Neubiberg/Munchen,¨ 1993), volume 423 of Lecture Notes in Econom. and Math. Systems, pages 8–21. Springer, Berlin, 1995. [825] Darinka Dentcheva and Andrzej Ruszczynski.´ Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [826] Darinka Dentcheva and Andrzej Ruszczynski.´ Optimization with stochastic dominance constraints. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [827] Darinka Dentcheva and Andrzej Ruszczynski.´ Portfolio optimization with stochastic dominance constraints. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [828] Darinka Dentcheva and Andrzej Ruszczynski.´ Convexification of stochastic ordering. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [829] Darinka Dentcheva and Andrzej Ruszczynski.´ Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints. Math. Program., 99(2, Ser. A):329–350, 2004. [830] Darinka Dentcheva and Andrzej Ruszczynski.´ Semi-infinite probabilistic optimization: first-order stochastic dominance constraints. Optimization, 53(5-6):583–601, 2004. [831] Michel Denuit and Claude Lefevre.` Stochastic s-(increasing) convexity. In Generalized convexity and generalized monotonicity (Karlovassi, 1999), pages 167–182. Springer, Berlin, 2001. [832] Michel Denuit, Claude Lefevre,` and Sergey Utev. Stochastic orderings of convex/concave-type on an arbitrary grid. Math. Oper. Res., 24(4):835–846, 1999. [833] Concetta A. DePaolo and David J. Rader, Jr. A heuristic algorithm for a chance constrained stochastic program. European J. Oper. Res., 176(1):27–45, 2007. [834] Cyrus Derman, Gerald J. Lieberman, and Sheldon M. Ross. A sequential stochastic assignment problem. Management Sci., Theory 18, 349-355, 1972.

47 [835] C.L. Dert. Asset Liability Management for Pension Funds, A Multistage Chance Constrained Programming Approach. PhD thesis, Erasmus University, Rotterdam, The Netherlands, 1995. [836] Luc P. Devroye. An expanding automaton for use in stochastic optimization. J. Cybern. Inf. Sci. 82-94 (1978)., 1977. [837] Luc P. Devroye. Progressive global random search of continuous functions. Math. Programming, 15(3):330–342, 1978. [838] Luc P. Devroye. Inequalities for the completion times of stochastic PERT networks. Math. Oper. Res. 4, 441-447, 1979. [839] I.P. Devyaterikov and A.I. Koshlan’. A method of solving constrained stochastic optimization problems. Autom. Remote Control 49, No.5, 628-632 translation from Avtom. Telemekh. 1988, No.5, 99-105 (1988)., 1988. [840] I.P. Devyaterikov and A.I. Koshlan. Stochastic optimization methods with constraints. Autom. Remote Control 49, No.4, 397-412 translation from Avtom. Telemekh. 1988, No.4, 3-21 (1988)., 1988. [841] A.S. Dexter, J.N.W. Yu, and W.T. Ziemba. Portfolio selection in a lognormal market when the investor has a power utility function: Computational results. In Stochastic programming, Proc. int. Conf., Oxford 1974, 507-523, 1980. [842] Ang Zhao Di. A constrained iterative stochastic algorithm. Acta Automat. Sinica, 11(3):251–257, 1985. [843] Nico Di Domenica, George Birbilis, Gautam Mitra, and Patrick Valente. Stochastic programming and scenario generation within a simualtion framework. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [844] A. Di Nola and S. Sessa. A Boolean model of deciding in fuzzy environment. RAIRO Automat., 14(4):363–374, 1980. With comments by A. Dussauchoy. [845] Josep Díaz, Mathew D. Penrose, Jordi Petit, and María Serna. Approximating layout problems on random geometric graphs. J. Algorithms, 39(1):78–116, 2001. [846] Boyan Dimitrov and Jr. Green, David. Stochastic optimization problems under incomplete information on distribution functions. Control Cybernet., 26(1):93–110, 1997. [847] W. Dinkelbach. Entscheidungsmodelle. W. de Gruyter, Berlin, 1982. (in German). [848] J. Dippon and J. Renz. Weighted means in stochastic approximation of minima. SIAM Journal of Control and Optimization, 35:1811–1827, 1997. [849] Jurgen¨ Dippon. Globally convergent stochastic optimization with optimal asymptotic distribution. J. Appl. Probab., 35(2):395–406, 1998. [850] L.C.W. Dixon. On on-line variable metric methods. In Survey of mathematical programming, Proc. int. Symp., Vol. 3, Budapest 1976, 421-428, 1980. [851] L.C.W. Dixon and L. James. On stochastic variable-metric methods. In Analysis and optimisation of stochastic systems (Proc. Internat. Conf., Univ. Oxford, Oxford, 1978), pages 243–256. Academic Press, London, 1980. [852] D.T. Dochev and V.I. Zhukovski. An s1-optimal solution of a multicriterial problem with uncertainty. Godishnik Vissh. Uchebn. Zaved. Prilozhna Mat., 23(2):9–26 (1988), 1987. [853] D.T. Dochev and V.I. Zhukovski. Sufficient conditions for p1-optimality with uncertainty. Godish- nik Vissh. Uchebn. Zaved. Prilozhna Mat., 23(1):19–30 (1988), 1987.

48 [854] Stefcho P. Dokov and David P. Morton. Higher-order upper bounds on the expectation of a convex function. Stochastic Programming E-Print Series, http://www.speps.org, 2002. [855] Steftcho P. Dokov and David P. Morton. Second-order lower bounds on the expectation of a convex function. Math. Oper. Res., 30(3):662–677, 2005. [856] V.A.Dolodarenko. The statement of a complex problem of optimal control over a dynamical system with combinatorial plan. In Applied problems of the dynamics of controlled movement, Collect. sci. Works, Kiev 1981, 119-127, 1981. [857] V.A. Dolodarenko and E.I. Fedan. Ueber eine Methode zur Loesung des Zuordnungsproblems mit nichtlinearer stochastischer Zielfunktion. Kibernetika, Kiev 1977, Nr. 2, 136-141, 1977. [858] V.A. Dolodarenko and V.S. Sen’kin. On an optimization problem under given probability of aim reaching. In Probabilistic-statistical methods for investigations of complex systems, Work Collect., Kiev 1976, 40-45, 1976. [859] V.O. Dolodarenko and E.I. Fedan. An allocation problem with non-linear stochastic objective function. Avtomatika, Kiev 1976, Nr. 3, 29-32, 1976. [860] Christopher J. Donohue and John R. Birge. An upper bound on the expected value of a non- increasing convex function with convex marginal return functions. Oper. Res. Lett., 18(5):213–221, 1996. [861] Christopher J. Donohue and John R. Birge. The abridged nested decomposition method for multistage stochastic linear programs with relatively complete recourse. Algorithmic Oper. Res., 1(1):20–30, 2006. [862] C. C. Y. Dorea and L. C. Zhao. Convergence of a random algorithm for function optimization. Numer. Funct. Anal. Optim., 20(9-10):825–833, 1999. [863] C.C.Y. Dorea. Stochastic algorithm for solving a set of inequalities. Numer. Funct. Anal. Optim., 10(9-10):937–945, 1989. [864] C.C.Y. Dorea. Stopping rules for a random optimization method. SIAM J. Control Optimization 28, No.4, 841-850, 1990. [865] C.C.Y. Dorea and C.R. Gonc¸alves. Alternative sampling strategy for a random optimization algorithm. J. Optim. Theory Appl., 78(2):401–407, 1993. [866] Chang C. Y. Dorea and Catia´ R. Gonc¸alves. Search schemes for random optimization algorithms that preserve the asymptotic distribution. J. Appl. Probab., 36(3):825–836, 1999. [867] Chang Chung Yu Dorea. Stationary distribution of Markov chains in rd with application to global random optimization. Bernoulli, 3(4):415–427, 1997. [868] Chang C.Y. Dorea. Limiting distribution for random optimization methods. SIAM J. Control Optim., 24(1):76–82, 1986. [869] Chang C.Y. Dorea. Effort associated with a class of random optimization methods. Math. Pro- gramming, 50(1 (Ser. A)):91–98, 1991. [870] Jan van Doremalen. Mean value analysis in multichain queueing networks: An iterative approximation. In Operations research, Proc. 12th Annu. Meet., Mannheim 1983, 441-448 , 1984. [871] A.A. Dorogovtsev. Stochastic analysis and a minimization problem. Ukrain.¨ Mat. Zh., 46(11):1568–1571, 1994. [872] P. Doschkinov. A distribution stability result for a stochastic optimal control problem. Optimization 18, 419-431, 1987.

49 [873] Julian Douglass, Owen Wu, and William T. Ziemba. Stock ownership decisions in dc pension plans. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [874] Mihai Dragomirescu. An algorithm for the minimum-risk problem of stochastic programming. Operations Res. 20, 154-164, 1972. [875] S.J. Drijver, W.K. Klein Haneveld, and M.H. van der Vlerk. Asset liability management modeling using multistage mixed-integer stochastic programming. Research Report 00E52, SOM, University of Groningen, 2000. [876] S.J. Drijver, W.K. Klein Haneveld, and M.H. van der Vlerk. ALM model for pension funds: numerical results for a prototype model. Research Report 02A44, SOM, University of Groningen, http://som.rug.nl, 2002. [877] S.J. Drijver, W.K. Klein Haneveld, and M.H. van der Vlerk. Asset Liability Management modeling using multi-stage mixed-integer Stochastic Programming. In B. Scherer, editor, Asset and Liability Management Tools: A Handbook for Best Practice, pages 309–324. Risk Books, London, 2003. [878] Moshe Dror. Modeling vehicle routing with uncertain demands as a stochastic program: Properties of the corresponding solution. Eur. J. Oper. Res. 64, No.3, 432-441, 1993. [879] Moshe Dror, Gilbert Laporte, and Pierre Trudeau. Vehicle routing with stochastic demands: properties and solution frameworks. Transportation Sci., 23(3):166–176, 1989. [880] Moshe Dror and Pierre Trudeau. Stochastic vehicle routing with modified savings algorithm. Eur. J. Oper. Res. 23, 228-235, 1986. [881] Didier Dubois. Linear programming with fuzzy data. In Analysis of fuzzy information, Vol. 3: Appl. eng. sci., 241-263, 1987. [882] Yu.A. Dubov. Necessary and sufficient conditions for Pareto-optimality in mean. Eng. Cybern. 17, No.6, 109-114 translation from Izv. Akad. Nauk SSSR, Tekh. Kibern. 1979, No.6, 137-141 (1979)., 1979. [883] Alan I. Duchan. A clarification and a new proof of the certainty equivalence theorem. Internat. econom. Review 15, 216-224, 1974. [884] Ewa Dudek-Dyduch and Tadeusz Dyduch. On optimization with random seeking. In Transactions of the Tenth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, Vol. A (Prague, 1986), pages 293–298. Reidel, Dordrecht, 1988. [885] Gunter Dueck and Tobias Scheuer. Threshold accepting: A general purpose optimization algorithm appearing superior to simulated annealing. J. Comput. Phys. 90, No.1, 161-175, 1990. [886] W. Duerr. Stochastische Programmierungsmodelle als Vektormaximumprobleme. In Proc. Oper. Res., DGU Ann. Meet. 1971, 189-199, 1972. [887] J. H. Dula,´ R. V. Helgason, and N. Venugopal. An algorithm for identifying the frame of a pointed finite conical hull. INFORMS J. Comput., 10(3):323–330, 1998. [888] Jose´ H. Dula.´ An upper bound on the expectation of simplicial functions of multivariate random variables. Math. Programming, 55(1, Ser. A):69–80, 1992. [889] Jose´ H. Dula.´ Bounds and approximations in stochastic linear programming. Investigacion´ Oper., 14(2-3):127–147, 1993. Workshop on Stochastic Optimization: the State of the Art (Havana, 1992). [890] Jose´ H. Dula.´ Designing a majorization scheme for the recourse function in two-stage stochastic linear programming. Comput. Optim. Appl., 1(4):399–414, 1993.

50 [891] Jose H. Dula and Rajluxmi V. Murthy. A Tchebysheff-type bound on the expectation of sublinear polyhedral functions. Oper. Res. 40, No.5, 914-922, 1992. [892] Vincentiu Dumitru and Florica Luban. On some optimization problems under uncertainty. Fuzzy Sets Syst. 18, 257-272, 1986. [893] J. Dupacovˇ a.´ In Studies on mathematical programming (Papers, Third Conf. Math. Programming, Matraf´ ured,¨ 1975), Budapest. [894] J. Dupacova. Stochastic programming models in banking. Tutorial Paper, IIASA Laxenburg, February 1991. [895] J. Dupacovˇ a.´ Minimax approach to stochastic linear programming and the moment problem. Se- lected results. Z. Angew. Math. Mech., 58(7):T466–T467, 1978. [896] J. Dupacovˇ a.´ Experience in stochastic programming models. In Survey of mathematical programming (Proc. Ninth Internat. Math. Programming Sympos., Budapest, 1976), Vol. 2, pages 99–105, Amsterdam, 1979. North-Holland. [897] J. Dupacovˇ a.´ Stability studies in stochastic programs with recourse. A special case. Z. Angew. Math. Mech., 62(5):T369–T370, 1982. [898] J. Dupacovˇ a.´ Stability in stochastic programming with recourse. Acta Univ. Carolin.—Math. Phys., 24(1):23–34, 1983. [899] J. Dupacovˇ a.´ Stability in stochastic programming with recourse-estimated parameters. Math. Programming, 28(1):72–83, 1984. [900] J. Dupacovˇ a.´ Stability in stochastic programming with recourse. Contaminated distributions. Math. Programming Stud., 27:133–144, 1986. Stochastic programming 84. I. [901] J. Dupacovˇ a.´ Stochastic Programming.MSˇ CSR,ˇ Prague, 1986. (in Czech). [902] J. Dupacova. Stochastic optimization models in banking. EMO, 27:201–234, 1991. In Czech. [903] J. Dupacova. Applications of stochastic programming in ﬁnance. In Atti del XVI convegno A.M.A.S.E.S., Treviso 1992, pages 13–30, 1992. [904] J. Dupacova. Stochastic programming models in banking & portfolio optimization under uncertainty. In W. Runggaldier, editor, Stochastic Processes: Applications in Mathematical Economics - Finance, Applied Mathematics Monographs 5, pages 19–20. C.N.R., 1992. [905] J. Dupacova. Bounds for stochastic programs in particular for recourse problems. Working paper WP-95-085, IIASA, Laxenburg, Austria, 1995. [906] J. Dupacova. Scenario based stochastic programs: Resistance with respect to sample. Annals of Oper. Res., 64:21–38, 1996. [907] J. Dupacova. Uncertainty about input data in portfolio management. In M. Bertocchi et al., editor, Modelling Techniques for Financial Markets and Bank Management, pages 17–33. Physica Verlag, 1996. [908] J. Dupacova. Input analysis for a bond portfolio management model. ZAMM, 77:541–542, 1997. [909] J. Dupacova. Moment bounds for stochastic programs in particular for recourse problems. In V. Benesˇ and J. Stˇ epˇ an,´ editors, Distributions with Given Marginals and Moment Problems (Proc. of the 3rd International Conference, Praha 1996), pages 199–204. Kluwer Acad. Publ, 1997. [910] J. Dupacova. Stochastic programming: Minimax approach. In C. A. Floudas & P. M. Pardalos, editor, Encyclopedia of Optimization, volume 5, pages 327–330. Kluwer, 2001.

51 [911] J. Dupacovˇ a.´ Stress testing via contamination. In Coping with uncertainty, volume 581 of Lecture Notes in Econom. and Math. Systems, pages 29–46. Springer, Berlin, 2006. [912] J. Dupacova and M. Bertocchi. From data to model and back to data: A bond portfolio management problem. EJOR, 134:261–278, 2001. [913] J. Dupacova, M. Bertocchi, and V. Moriggia. Sensitivity analysis on inputs for a bond portfolio management model. In P. Albrecht, editor, Aktuarielle Ansatze¨ fur¨ Finanz-Risiken AFIR 1996, Proc. of the VIth AFIR Colloquium, Nuremberg, pages 783–793. VVW Karlsruhe, 1996. See also Technical Report 16, Univ. of Bergamo, 1996. [914] J. Dupacova, M. Bertocchi, and V. Moriggia. Postoptimality for a bond portfolio management model. In C. Zopounidias, editor, New Operational Approaches in Financial Modelling (Proc. of the 19th meeting of EURO WGFM, Chania, Crete, 1996), pages 49–62, Heidelberg, 1997. Physica Verlag. See also Technical Report No. 13, Univ. of Bergamo 1997. [915] J. Dupacova, M. Bertocchi, and V. Moriggia. Sensitivity analysis for a bond portfolio management model for the italian market. Cybernetics, 29:595–615, 2000. [916] J. Dupacova, M. Bertocchi, and V. Moriggia. Sensitivity analysis of a bond portfolio management model for the italian market. Control & Dynamics, 29:595–615, 2000. [917] J. Dupacova, M. Bertocchi, and V. Moriggia. Sensitivity of a bond portfolio’s behavior with respect to random movements in yield curve: A simulation study. Ann. Oper. Res., 99:267–286, 2000. [918] J. Dupacova, M. Bertocchi, and V. Moriggia. Postoptimality for scenario based ﬁnancial models with an application to bond portfolio management. In W. Ziemba and J. Mulvey, editors, World Wide Asset and Liability Management. Cambridge Univ. Press, To appear. [919] J. Dupacova, P. Charamza, and J. Madl.´ On stochastic aspects of a metal cutting problem. In K. Marti and P. Kall, editors, Proc. of 2nd GAMM/IFIP Workshop ‘Stochastic Optimization: Nu- merical Techniques and Engineering Applications’, LN in Economics and Math. Systems 423, pages 196–209. Springer, 1995. [920] J. Dupacova, A. Gaivoronski, Z. Kos, and T. Szantai. Stochastic programming in water management: A case study and a comparison of solution techniques. EJOR, 52:28–44, 1991. [921] J. Dupacovˇ a,´ J. Hurt, and J. Stˇ epˇ an.´ Stochastic Modeling in Economics and Finance, volume 75 of Applied Optimization. Kluver Acad. Publ., 2002. [922] J. Dupacova, M. Bertocchi J. Abaffy, and V. Moriggia. Generating scenarios for bond portfolios. Bulletin of the Czech Econometric Society, 11:3–27, 2000. [923] J. Dupacova, J. Madl,´ and P.Charamza. A mathematical model for optimization of cutting conditions in machining. In U. Derigs, A. Bachem, and A. Drexl, editors, OR-proceedings 1994, pages 28–32. Springer, 1995. [924] J. Dupacovˇ a´ and K. Sladky.´ Comparison of multistage stochastic programs with recourse and stochastic dynamic programs with discrete time. ZAMM Z. Angew. Math. Mech., 82(11-12):753– 765, 2002. 4th GAMM-Workshop “Stochastic Models and Control Theory” (Lutherstadt Witten- berg, 2001). [925] Jitka Dupacovˇ a.´ Minimax stochastic programs with nonconvex nonseparable penalty functions. In Progress in operations research, Vols. I, II (Proc. Sixth Hungarian Conf., Eger, 1974), pages 303–316. Colloq. Math. Soc. Janos´ Bolyai, Vol. 12, Amsterdam, 1976. North-Holland. [926] Jitka Dupacovˇ a.´ The minimax problem of stochastic linear programming and the moment problem. Ekonom.-Mat. Obzor, 13(3):279–307, 1977.

52 [927] Jitka Dupacovˇ a.´ Minimax stochastic programs with nonseparable penalties. In Optimization techniques (Proc. Ninth IFIP Conf., Warsaw, 1979), Part 1, volume 22 of Lecture Notes in Control and Information Sci., pages 157–163, Berlin, 1980. Springer. [928] Jitka Dupacovˇ a.´ Water resources system modelling using stochastic programming with recourse. In Recent results in stochastic programming (Proc. Meeting, Oberwolfach, 1979), volume 179 of Lecture Notes in Econom. and Math. Systems, pages 121–133, Berlin, 1980. Springer. [929] Jitka Dupacovˇ a.´ Stability in stochastic programming—probabilistic constraints. In Stochastic optimization (Kiev, 1984), volume 81 of Lecture Notes in Control and Inform. Sci., pages 314–325. Springer, Berlin, 1986. [930] Jitka Dupacovˇ a.´ The minimax approach to stochastic programming and an illustrative application. Stochastics, 20(1):73–88, 1987. [931] Jitka Dupacovˇ a.´ On some connections between parametric and stochastic programming. In Para- metric optimization and related topics (Plaue, 1985), volume 35 of Math. Res., pages 74–81. Akademie-Verlag, Berlin, 1987. [932] Jitka Dupacovˇ a.´ Stochastic programming with incomplete information: a survey of results on postoptimization and sensitivity analysis. Optimization, 18(4):507–532, 1987. [933] Jitka Dupacovˇ a.´ On nonnormal asymptotic behavior of optimal solutions of stochastic programming problems: the parametric case. In Proceedings of the Fourth Prague Symposium on Asymp- totic Statistics (Prague, 1988), pages 205–214, Prague, 1989. Charles Univ. [934] Jitka Dupacovˇ a.´ Stochastic programming—model building and selected applications. Investigacion´ Oper., 10(3):119–134, 1989. [935] Jitka Dupacovˇ a.´ Stability and sensitivity analysis for stochastic programming. Ann. Oper. Res., 27(1-4):115–142, 1990. [936] Jitka Dupacovˇ a.´ On nonnormal asymptotic behavior of optimal solutions for stochastic programming problems and on related problems of mathematical statistics. Kybernetika (Prague), 27(1):38–52, 1991. [937] Jitka Dupacovˇ a.´ On statistical sensitivity analysis in stochastic programming. Ann. Oper. Res., 30(1-4):199–214, 1991. Stochastic programming, Part I (Ann Arbor, MI, 1989). [938] Jitka Dupacovˇ a.´ Stochastic optimization models in banking. Ekonom.-Mat. Obzor, 27(3):201–234, 1991. [939] Jitka Dupacovˇ a.´ On interval estimates for optimal value of stochastic programs. In P. Kall, editor, System modelling and optimization (Zurich, 1991), volume 180 of Lecture Notes in Control and Inform. Sci., pages 556–563. Springer, Berlin, 1992. [940] Jitka Dupacovˇ a.´ Applications of stochastic programming under incomplete information. J. Comput. Appl. Math., 56(1-2):113–125, 1994. Stochastic programming: stability, numerical methods and applications (Gosen, 1992). [941] Jitka Dupacovˇ a.´ Multistage stochastic programs: the state-of-the-art and selected bibliography. Kybernetika (Prague), 31(2):151–174, 1995. [942] Jitka Dupacovˇ a.´ Postoptimality for multistage stochastic linear programs. Ann. Oper. Res., 56:65– 78, 1995. Stochastic programming (Udine, 1992). [943] Jitka Dupacovˇ a.´ Stochastic programming: Approximation via scenarios. In Proceedings of 3rd Caribbean Conference on Approximation and Optimization. EMIS Master Server http://www. emis.de/proceedings/index.html, 1995.

53 [944] Jitka Dupacovˇ a.´ Scenario-based stochastic programs: resistance with respect to sample. Ann. Oper. Res., 64:21–38, 1996. Stochastic programming, algorithms and models (Lillehammer, 1994). [945] Jitka Dupacovˇ a.´ Postoptimality analysis for scenario based stochastic programs: a survey. In J. Guddat et al., editor, Parametric optimization and related topics, IV (Enschede, 1995), volume 9 of Approx. Optim., pages 43–57, Frankfurt am Main, 1997. Lang. [946] Jitka Dupacovˇ a.´ Stochastic programming: approximation via scenarios. In Proceedings of the 3rd International Conference on Approximation and Optimization in the Caribbean (Puebla, 1995), page 20 pp. (electronic). Benemerita´ Univ. Auton.´ Puebla, Puebla, 1997. [947] Jitka Dupacovˇ a.´ Reflections on robust optimization. In Stochastic programming methods and technical applications (Neubiberg/Munich, 1996), pages 111–127. Springer, Berlin, 1998. [948] Jitka Dupacovˇ a.´ Stochastic programming: Approximation via scenarios. Aportaciones Mathemat- icas, Ser. Communicationes, 24:77–94, 1998. [949] Jitka Dupacovˇ a.´ Portfolio optimization via stochastic programming: methods of output analysis. Math. Methods Oper. Res., 50(2):245–270, 1999. Financial optimization. [950] Jitka Dupacovˇ a.´ Stability properties of a bond portfolio management problem. Ann. Oper Res., 99:251–265 (2001), 2000. Applied mathematical programming and modeling, IV (Limassol, 1998). [951] Jitka Dupacovˇ a.´ Output analysis for approximated stochastic programs. In Stochastic optimization: algorithms and applications (Gainesville, FL, 2000), volume 54 of Appl. Optim., pages 1–29. Kluwer Acad. Publ., Dordrecht, 2001. [952] Jitka Dupacovˇ a.´ Applications of stochastic programming: achievements and questions. European J. Oper. Res., 140(2):281–290, 2002. O.R. for a united Europe (Budapest, 2000). [953] Jitka Dupacovˇ a.´ Reflections on output analysis for multistage stochastic linear programs. In Dy- namic stochastic optimization (Laxenburg, 2002), volume 532 of Lecture Notes in Econom. and Math. Systems, pages 3–20. Springer, Berlin, 2004. [954] Jitka Dupacova.´ Uncertainties in stochastic programming models: The minimax approach. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algo- rithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [955] Jitka Dupacova.´ Contamination for multistage stochastic programs. Stochastic Programming E- Print Series, http://www.speps.org, 2006. [956] Jitka Dupacovˇ a´ and Marida Bertocchi. Management of bond portfolios via stochastic programming—postoptimality and sensitivity analysis. In System modelling and optimization (Prague, 1995), pages 574–581. Chapman & Hall, London, 1996. [957] Jitka Dupacovˇ a,´ Giorgio Consigli, and Stein W. Wallace. Scenarios for multistage stochastic programs. Ann. Oper Res., 100:25–53 (2001), 2000. Research in stochastic programming (Vancouver, BC, 1998). [958] Jitka Dupacovˇ a,´ Nicole Growe-Kuska,¨ and Werner Romisch.¨ Scenario reduction in stochastic programming: An approach using probability metrics. Stochastic Programming E-Print Series, http://www.speps.org, to appear in Math. Progr., 2000. [959] Jitka Dupacova and Zdenek Kos. Chance-constrained and simulation models of water resources systems. Ekon.-Mat. Obz. 15, 178-191, 1979.

54 [960] Jitka Dupacova´ and Jan Polivka. Asset-liability management for czech pension funds using stochastic programming. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [961] Jitka Dupacova´ and Jan Polivka. Stress testing for var an cvar. Stochastic Programming E-Print Series, http://www.speps.org, 2005. [962] Jitka Dupacova´ and Pavel Popela. Melt control. Stochastic Programming E-Print Series, http: //www.speps.org, 2004. [963] Jitka Dupacovˇ a´ and Pavel Popela. Melt control: charge optimization via stochastic programming. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 277–297. SIAM, Philadelphia, PA, 2005. [964] Jitka Dupacovˇ a´ and Roger Wets. Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems. Ann. Statist., 16(4):1517–1549, 1988. [965] Paul Dupuis and Rahul Simha. On sampling controlled stochastic approximation. IEEE Trans. Autom. Control 36, No.8, 915-924, 1991. [966] G. Duru. Planiﬁcation de la production en avenir aleatoire. Publ. econometr., Lyon 4, 381-411, 1971. [967] G. Duru. Programme stochastique gen´ eralis´ e´ a` un etage.´ Publ. Econom´ etriques´ , 5:17–36, 1972. [968] Prajit K. Dutta. What do discounted optima converge to? A theory of discount rate asymptotics in economic models. J. Econom. Theory, 55(1):64–94, 1991. [969] Prajit K. Dutta and Mukul Majumdar. Limit integration theorems for monotone functions and parametric continuity in zero sum stochastic games. Nonlinear World, 1(1):73–91, 1994. [970] Shane Dye. Subtree decomposition for multistage stochastic programs. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [971] Shane Dye. Subtree decomposition for multistage stochastic programs. In S. Albers, R.H. Mohring,¨ G.Ch. Pﬂug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [972] Shane Dye, Leen Stougie, and Asgeir Tomasgard. The stochastic single node service provision problem. Stochastic Programming E-Print Series, http://www.speps.org, 2002. [973] M. Dyer and L. Stougie. Stochastic programming problems: Complexity and approximability. in preparation. [974] Martin Dyer and Alan Frieze. Probabilistic analysis of the generalised assignment problem. Math. Programming, 55(2, Ser. A):169–181, 1992. [975] Martin Dyer and Leen Stougie. Computational complexity of stochastic programming problems. Math. Program., 106(3, Ser. A):423–432, 2006. [976] M.E. Dyer, A.M. Frieze, and C.J.H. McDiarmid. On linear programs with random costs. Math. Program. 35, 3-16, 1986. [977] Richard L. Dykstra. Computational aspects of I -projections. J. Statist. Comput. Simulation, 21(3- 4):265–274, 1985. [978] Richard L. Dykstra. An iterative procedure for obtaining I -projections onto the intersection of convex sets. Ann. Probab., 13(3):975–984, 1985. [979] E.B. Dynkin. Probabilistic concave dynamic programming. Mat. Sb. (N.S.), 87(129):490–503, 1972.

55 [980] E.B. Dynkin. Optimal programs and stimulating prices in the stochastic models of economic growth. In Math. Models Econ., Proc. Sympos. math. Meth. Econ. and Conf. von Neumann Models, Warszawa 1972, 207-218, 1974. [981] E.B. Dynkin and A.A. Yushkevich. Controllable Markov processes and their applications. (Up- ravlyaemye markovskie protsessy i ikh prilozheniya). Moskva: ”Nauka”, 1975. [982] R.G. Dyson. Minimax solutions to stochastic programs - an aid to planning under uncertainty. J. Oper. Res. Soc. 29, 691-696, 1978. [983] Jr. Eberl, W. and O. Moeschlin. On measurability in stochastic programming. In Probability and statistical decision theory, Vol. A (Bad Tatzmannsdorf, 1983), pages 97–105, Dordrecht, 1985. Reidel. [984] David Edelman. On the financial value of information. Ann. Oper Res., 100:123–132 (2001), 2000. Research in stochastic programming (Vancouver, BC, 1998). [985] Chanaka Edirisinghe, Derek Atkins, and Paul Iyogun. Bounds on stochastic convex allocation problems. Appl. Stochastic Models Data Anal., 10(2):123–140, 1994. [986] N. C. P. Edirisinghe. Bound-based approximations in multistage stochastic programming: nonanticipativity aggregation. Ann. Oper. Res., 85:103–127, 1999. Stochastic programming. State of the art, 1998 (Vancouver, BC). [987] N. C. P. Edirisinghe, E. I. Patterson, and N. Saadouli. Capacity planning model for a multipur- pose water reservoir with target-priority operation. Ann. Oper. Res., 100:273–303 (2001), 2000. Research in stochastic programming (Vancouver, BC, 1998). [988] N.C.P. Edirisinghe and G.-M. You. Second-order scenario approximation and refinement in optimization under uncertainty. Ann. Oper. Res., 64:143–178, 1996. Stochastic programming, algorithms and models (Lillehammer, 1994). [989] N.C.P. Edirisinghe and W.T. Ziemba. Tight bounds for stochastic convex programs. Oper. Res., 40(4):660–677, 1992. [990] N.C.P. Edirisinghe and W.T. Ziemba. Bounding the expectation of a saddle function with application to stochastic programming. Math. Oper. Res., 19(2):314–340, 1994. [991] N.C.P. Edirisinghe and W.T. Ziemba. Bounds for two-stage stochastic programs with fixed recourse. Math. Oper. Res., 19(2):292–313, 1994. [992] N.C.P. Edirisinghe and W.T. Ziemba. Implementing bounds-based approximations in convex- concave two-stage stochastic programming. Math. Programming, 75(2, Ser. B):295–325, 1996. Approximation and computation in stochastic programming. [993] Ivan Edissonov. The new ARSTI optimization method: adaptive random search with translating intervals. Amer. J. Math. Management Sci., 14(3-4):143–166, 1994. [994] J. Edwards. A proposed standard input format for computer codes which solve stochastic programs with recourse. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 215–227. Springer, Berlin, 1988. [995] V.M. Efimov. A stochastic model of long term planning. In Theory of optimal solutions (Proc. Sem., Kiev, 1969), No. 3 (Russian), pages 36–45, Kiev, 1969. Akad. Nauk Ukrain. SSR. [996] V.M. Efimov. Untersuchung stochastischer Extremalprobleme mittels der Funktionalanalysis. Kibernetika, Kiev 1970, No.3, 63-68, 1970.

56 [997] Pavlos S. Efraimidis and Paul G. Spirakis. Combinatorial randomized rounding: boosting randomized rounding with combinatorial arguments. In Stochastic optimization: algorithms and applications (Gainesville, FL, 2000), pages 31–53. Kluwer Acad. Publ., Dordrecht, 2001. [998] V. A. Efremov. A numerical algorithm for solving a bilinear problem of quantile optimization. [999] Jan Ehrhoff, Sven Grothklags, and Ulf Lorenz. Disruption Management and Planning with Un- certainties in Aircraft Planning. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [1000] Andreas Eichhorn and Werner Romisch.¨ Polyhedral risk measures in stochastic programming. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [1001] Andreas Eichhorn and Werner Romisch.¨ Polyhedral risk measures in stochastic programming. SIAM J. Optim., 16(1):69–95 (electronic), 2005. [1002] Andreas Eichhorn and Werner Romisch.¨ Stochastic integer programming. Stochastic Programming E-Print Series, http://www.speps.org, 2005. [1003] Andreas Eichhorn and Werner Romisch.¨ Stability of multistage stochastic programs incorporating polyhedral risk measures. Stochastic Programming E-Print Series, http://www.speps.org, 2006. [1004] Andreas Eichhorn and Werner Romisch.¨ Stochastic integer programming: limit theorems and confidence intervals. Math. Oper. Res., 32(1):118–135, 2007. [1005] Andreas Eichhorn, Werner Romisch,¨ and Isabel Wegner. Polyhedral Risk Measures and Lagrangian Relaxation in Electricity Portfolio Optimization. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Infor- mation, http://www.dagstuhl.de/05031, 2005. [1006] Mark J. Eisner, Robert S. Kaplan, and John V. Soden. Admissible decision rules for the E-model of chance-constrained programming. Management Sci., Theory 17, 337-353, 1971.

[1007] Mark J. Eisner and Paul Olsen. Duality for stochastic programming interpreted as L. P. in Lp space. SIAM J. appl. Math. 28, 779-792, 1975. [1008] Mark J. Eisner and Paul Olsen. Duality in probabilistic programming. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 147–158, London, 1980. Academic Press. [1009] Abou-Zaid H. El-Banna and Ebrahim A. Youness. On stability of stochastic multiobjective programming problems with random coefﬁcients in the objective functions. Matematiche (Catania), 49(1):3–9 (1995), 1994. [1010] M.C. El Bouamri. Minimisation en cascade des programmes convexes a` temps discret et a` con- trainte convexe non-anticipative. Travaux Sem.´ Anal. Convexe, 12(2):exp. no. 14, 23, 1982. [1011] M. El-Sayed Wahed. Neural network representation of stochastic quadratic programming problems when bi ’s and c j ’s follow goint distribution. J. Inst. Math. Comput. Sci. Comput. Sci. Ser., 15(2):263–276, 2004. [1012] D.F. Elliott and D.D. Sworder. A variable metric technique for parameter optimization. Automatica- J. IFAC, 5:811–816, 1969. [1013] R.S. Ellis and R.W. Rishel. An application of stochastic optimal control theory to the optimal rescheduling of airplanes. IEEE Trans. Automatic Control, AC-19:139–142, 1974.

57 [1014] Paul M. Ellner and Robert M. Stark. On the distribution of the optimal value for a class of stochastic geometric programs. Naval Res. Logist. Quart., 27(4):549–571, 1980. [1015] E.A. Elsayed and Mohammed Ettouney. Perturbation analysis of linear programming problems with random parameters. Comput. Oper. Res. 21, No.2, 211-224, 1994. [1016] K. H. Elster and R. Elster. Optimization of c-orthogonal posynomials. Acta Math. Vietnam., 22(1):71–105, 1997. [1017] V.A. Emelicevˇ and A.M. Kononenko. The number of plans for a multi-index selection problem. Dokl. Akad. Nauk BSSR, 18:677–680, 763, 1974. [1018] A.K. Enaleev and D.A. Novikov. Optimal stimulation mechanisms in an active system with probabilistic uncertainty. I. Avtomat. i Telemekh., 9:117–126, 1995. [1019] Sebastian Engell, Andreas Markert,¨ Guido Sand, Rudiger¨ Schultz, and Christian Schulz. Online scheduling of multiproduct batch plants under uncertainty. In Online optimization of large scale systems, pages 649–676. Springer, Berlin, 2001. [1020] Heinz W. Engl. Existence of measurable optima in stochastic nonlinear programming and control. Appl. Math. Optimization 5, 271-281, 1979. [1021] Katherine Bennett Ensor and Peter W. Glynn. Stochastic optimization via grid search. In Math- ematics of stochastic manufacturing systems (Williamsburg, VA, 1996), volume 33 of Lectures in Appl. Math., pages 89–100, Providence, RI, 1997. Amer. Math. Soc. [1022] Robert Entriken. Language constructs for modeling stochastic linear programs. Ann. Oper Res., 104:49–66 (2002), 2001. Modeling languages and systems. [1023] Leah Epstein and Asaf Levin. Tracking mobile users. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [1024] Leah Epstein and Rob van Stee. Online scheduling of splittable tasks. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [1025] E. Erdogan and G. Iyengar. Ambiguous chance constrained problems and robust optimization. Stochastic Programming E-Print Series, http://www.speps.org, 2005. [1026] E. Erdogan and G. Iyengar. Ambiguous chance constrained problems and robust optimization. Math. Program., 107(1-2, Ser. B):37–61, 2006. [1027] E. Erdogan and G. Iyengar. On two-stage convex chance constrained problems. Stochastic Pro- gramming E-Print Series, http://www.speps.org, 2006. [1028] I.I. Eremin and Vl.D. Mazurov. Nonstationary processes for mathematical programming problems under the conditions of poorly formalized constraints and incomplete defining information. In Optim. Techn., IFIP techn. Conf. Novosibirsk 1974, Lect. Notes Comput. Sci. 27, 37-41, 1975. [1029] I.I. Eremin¨ and A.A. Vatolin. Duality in improper mathematical programming problems under uncertainty. In Stochastic optimization (Kiev, 1984), volume 81 of Lecture Notes in Control and Inform. Sci., pages 326–333. Springer, Berlin, 1986. [1030] Horst Erfurth and Claus Bendzulla. Die numerische Loesung eines speziellen Systems 1. Ordnung mit verteilten Parametern. (Numerical solution of a special first-order system with distributed parameters). Wiss. Z. Tech. Hochschule Chemie Carl Schorlemmer Leuna-Merseburg 13, 364- 367, 1971.

58 [1031] S.M. Ermakov and A.A. Zhiglyavskij. On a random search of a global extremum. Teor. Veroyatn. Primen. 28, No.1, 129-134, 1983. [1032] S.M. Ermakov and A.A. Zhiglyavskij. On random search for a global extremum. Theory Probab. Appl. 28, 136-141, 1984. [1033] S.M. Ermakov, A.A. Zhiglyavskij, and V.N.Solntsev. On a random search scheme for the extremum of functions. In Monte Carlo methods in numerical mathematics and mathematical physics, Pap. VI. All-Union Conf., April 1979, Part 1, Novosibirsk 1979, 17-24 , 1979. [1034] O.V. Ermolenko. The solution of two-stage stochastic problems with nonconvex functions. Kiber- netika (Kiev), 3:100–102, 1976. [1035] Ju. M. Ermol’ev. Conditions for optimality in stochastic programming problems. In Theory of optimal solutions (Proc. Sem., Kiev, 1969), No. 1 (Russian), pages 36–44, Kiev, 1969. Akad. Nauk Ukrain. SSR. [1036] Ju. M. Ermol’ev. The method of generalized stochastic gradients and stochastic quasi-Fejer´ sequences. Kibernetika (Kiev), 2:73–83, 1969. [1037] Ju. M. Ermol’ev. A certain general problem of stochastic programming. Kibernetika (Kiev), 3:47– 50, 1971. [1038] Ju. M. Ermol’ev. The convergence of random quasi-Fejer´ sequences. Kibernetika (Kiev), 4:70–71, 1971. [1039] Ju. M. Ermol’ev. A method of generalized stochastic gradients, and its applications. In Proceed- ings of the Fourth All-Union Conference on Automatic Control—Engineering Cybernetics (Tbil- isi, 1968), Vol. 1: Optimal and adaptive systems (Russian), pages 230–236, 310. Izdat. “Nauka”, Moscow, 1972. [1040] Ju. M. Ermol’ev. Stochastic models, and optimization methods. Kibernetika (Kiev), 4:109–119, 1975. [1041] Ju. M. Ermol’ev and A.M. Gupal. An analogue of the linearization method in problems of the minimization of nondifferentiable functions. Kibernetika (Kiev), 1:65–68, 1978. [1042] Ju. M. Ermol’ev and A.I. Jastremskii. Stokhasticheskie modeli i metody v ekonomicheskom` planirovanii. “Nauka”, Moscow, 1979. Ekonomiko-Matematicheskaya` Biblioteka. [Mathemati- cal Economics Library]. [1043] Ju. M. Ermol’ev and Ju. M. Kaniovskii. Asymptotic properties of some stochastic programming methods with constant step. Zh. Vychisl. Mat. i Mat. Fiz., 19(2):356–366, 556, 1979. [1044] Ju. M. Ermol’ev and T.P. Mar’janovic.ˇ Optimization and simulation. Problemy Kibernet., 27:111– 125, 294, 1973. A collection consisting mainly of papers presented at the Second All-Union Con- ference on Problems of Theoretical Cybernetics (Novosibirsk, 1971). [1045] Ju. M. Ermol’ev and I.M. Mel’nik. Stochastic programming methods with a ﬁnite number of tests. Kibernetika (Kiev), 4:52–54, 1974. [1046] Ju. M. Ermol’ev and F. Mirzoahmedov. Direct methods of stochastic programming in problems of inventory planning. Kibernetika (Kiev), 6:74–81, 1976. [1047] Ju. M. Ermol’ev and E.A. Nurminskii. Extremal problems of statistics, and numerical methods for stochastic programming. In Certain questions on simulation and systems control (Russian), pages 31–52. Izdat. “Naukova Dumka”, Kiev, 1973. [1048] Ju. M. Ermol’ev and N.Z. Sor.ˇ A method of random search for a two step problem of stochastic programming and its generalization. Kibernetika (Kiev), 1:90–92, 1968.

59 [1049] Ju. M. Ermol’ev and A.D. Tuniev. Direct methods of solution of certain problems of stochastic programming. Kibernetika (Kiev), 4:100–102, 1968. [1050] Ju. M. Ermol’ev and P.I. Vercenko.ˇ The linearization method in limit extremal problems. Kiber- netika (Kiev), 2:65–69, 1976. [1051] Ju.M. Ermol’ev. Ueber einige Probleme der stochastischen Programmierung. Kibernetika, Kiev 1970, No.1, 1-5, 1970. [1052] Ju.M. Ermol’ev. Ueber ein allgemeines Problem der stochastischen Programmierung. Kibernetika, Kiev 1971, Nr. 3, 47-50, 1971. [1053] Ju.M. Ermol’ev. Stochastische Modelle und Optimierungsmethoden. Kibernetika, Kiev 1975, Nr. 4, 109-119, 1975. [1054] Ju.M. Ermol’ev and T.P. Mar’janovic. Optimierung und Modellierung. Probl. Kibernetiki 27, 111-125, 1973. [1055] Ju.M. Ermol’ev and I.M. Mel’nik. Ueber Methoden der stochastischen Programmierung mit einer endlichen Zahl von Proben. Kibernetika, Kiev 1974, Nr. 4, 52-54, 1974. [1056] Ju.M. Ermol’ev and F. Mirzoahmedov. Direkte Methoden der stochastischen Programmierung in Problemen der Vorratsplanung. Kibernetika, Kiev 1976, No.6, 74-81, 1976. [1057] Ju.M. Ermol’ev and A.D. Tuniev. Random Fejer and quasi-Fejer sequences. Select. Translat. math. Statist. Probab. 13, 143-148, 1973. [1058] Yu. M. Ermol’ev. The stochastic quasigradient methods and their application to the stochastic programming problems with nonsmooth functions. In Survey of mathematical programming (Proc. Ninth Internat. Math. Programming Sympos., Budapest, 1976), Vol. 2, pages 107–115, Amsterdam, 1979. North-Holland. [1059] Yu. M. Ermol’ev and A.A. Gaivoronskii. Stochastic methods for solving minimax problems. Cy- bernetics, 19(4):550–559 (1984), 1983. [1060] Yu. M. Ermol’ev and Ts. Kh. Nedeva. Questions of the stability of the solution of stochastic programming problems. In Methods of investigation of extremal problems, pages 29–34, 120, Kiev, 1981. Akad. Nauk Ukrain. SSR Inst. Kibernet. [1061] Yu. M. Ermol0ev and V. I. Norkin. On the nonstationary law of large numbers for dependent random variables and its application to stochastic optimization. Kibernet. Sistem. Anal., (4):94–106, 190, 1998. [1062] Yu. M. Ermol0ev and V. I. Norkin. The stochastic generalized gradient method for solving nonconvex nonsmooth problems of stochastic optimization. Kibernet. Sistem. Anal., (2):50–71, 187, 1998. [1063] Yu.M. Ermol’ev. Methods of stochastic programming. (Metody stokhasticheskogo programmirovaniya). Optimizatsiya i Issledovanie Operatsij. Moskva: Izdatel’stvo ”Nauka”, Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury., 1976. [1064] Yu.M. Ermol’ev and Yu.M. Kaniovskij. Asymptotische Eigenschaften gewisser Methoden der stochastischen Programmierung mit konstantem Schritt. Zh. Vychisl. Mat. Mat. Fiz. 19, 356-366, 1979. [1065] Yu.M. Ermol’ev and I.N. Kovalenko, editors. Mathematical methods in operations research and reliability theory. (Matematicheskie methody issledovaniya operatsij i teorii nadezhnosti). Kiev: Institut Kibernetiki AN USSR., 1978.

60 [1066] Yu.M. Ermol’ev, I.I. Lyashko, V.S. Mikhalevich, and V.I. Tyuptya. Mathematical methods in the investigation of operations. Textbook for universities. (Matematicheskie metody issledovaniya operatsij. Uchebnoe posobie dlya vuzov.). Kiev: Izdatel’skoe Ob’edinenie ”Vishcha Shkola”., 1979. [1067] Yu.M. Ermol’ev and Ts.Kh. Nedeva. Stability questions of the solution for problems of stochastic programming. In Investigation methods for extremal problems, Collect. Artic., Kiev 1981, 29-34, 1981. [1068] Yu.M. Ermol’ev and A.I. Yastremskij. Stochastic models and methods in economic planning. (Stokhasticheskie modeli i metody v ehkonomicheskom planirovanii). Ehkonomiko- Matematicheskaya Biblioteka. Moskva: ”Nauka”., 1979. [1069] Ermol’ev, Yu. M. Metody stokhasticheskogo programmirovaniya. Izdat. “Nauka”, Moscow, 1976. Optimizatsiyaa i Issledovanie Operatsii. [Monographs in Optimization and Operations Research]. [1070] T.Yu. Ermol’eva. Asymptotic behavior of regression estimators of stochastic processes with prior inequality constraints. Cybernetics 25, No.4, 525-530 translation from Kibernetika 1989, No.4, 86-89 (1989)., 1989. [1071] Y. M. Ermoliev, T. Y. Ermolieva, G. J. MacDonald, and V. I. Norkin. Insurability of catastrophic risks: the stochastic optimization model. Optimization, 47(3-4):251–265, 2000. Numerical methods for stochastic optimization and real-time control of robots (Neubiberg/Munich, 1998). [1072] Y. M. Ermoliev, T. Y. Ermolieva, G. J. MacDonald, and V. I. Norkin. Stochastic optimization of insurance portfolios for managing exposure to catastrophic risks. Ann. Oper Res., 99:207–225 (2001), 2000. Applied mathematical programming and modeling, IV (Limassol, 1998). [1073] Y.M. Ermoliev. Aspects of optimization and adaptation. In Stochastic phenomena and chaotic behaviour in complex systems (Flattnitz, 1983), volume 21 of Springer Ser. Synergetics, pages 13–16. Springer, Berlin, 1984. [1074] Y.M. Ermoliev and G. Leonardi. Some proposals for stochastic facility location models. Math. Modelling, 3(5):407–420, 1982. [1075] Y.M. Ermoliev, V.I. Norkin, and R.J-B. Wets. The minimization of semicontinuous functions: molliﬁer subgradients. SIAM Journal on Control and Optimization, 33(1):149–167, 1995. [1076] Yu. Ermoliev. Random optimization and stochastic programming. In Colloq. Methods Optim. Novosibirsk USSR 1968, Lecture Notes Math. 112, 104-115, 1970. [1077] Yu. Ermoliev. Stochastic quasigradient methods. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 141–185. Springer, Berlin, 1988. [1078] Yu. Ermoliev, A. Gaivoronski, and C. Nedeva. Stochastic optimization problems with incomplete information on distribution functions. SIAM J. Control Optim., 23(5):697–716, 1985. [1079] Yu. Ermoliev, S. Uryasev, and J. Wessels. On optimization of unreliable material ﬂow systems. In Probabilistic constrained optimization, volume 49 of Nonconvex Optim. Appl., pages 45–66. Kluwer Acad. Publ., Dordrecht, 2000. [1080] Yu. Ermoliev and R. Wets. Stochastic programming, an introduction. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 1–32. Springer, Berlin, 1988. [1081] Yu. Ermoliev and R.J-B. Wets. Numerical Techniques for Stochastic Optimization. Springer-Verlag, Berlin etc., 1988. [1082] Yu. M. Ermoliev. Methods of nondifferentiable and stochastic optimization and their applications. In Progress in nondifferentiable optimization, volume 8 of IIASA Collaborative Proc. Ser. CP-82, pages 5–27, Laxenburg, 1982. Internat. Inst. Appl. Systems Anal.

61 [1083] Yuri Ermoliev. Stochastic quasigradient methods and their application to system optimization. Stochastics, 9(1-2):1–36, 1983. [1084] Yuri Ermoliev and Vladimir Norkin. On constrained discontinuous optimization. In Stochas- tic programming methods and technical applications (Neubiberg/Munich, 1996), pages 128–144. Springer, Berlin, 1998. [1085] Yuri Ermoliev and Vladimir Norkin. Stochastic optimization of risk functions via parametric smoothing. In Dynamic stochastic optimization (Laxenburg, 2002), volume 532 of Lecture Notes in Econom. and Math. Systems, pages 225–247. Springer, Berlin, 2004. [1086] Yuri M. Ermoliev and Vladimir I. Norkin. Normalized convergence in stochastic optimization. Ann. Oper. Res., 30(1-4):187–198, 1991. Stochastic programming, Part I (Ann Arbor, MI, 1989). [1087] Yury M. Ermoliev and Alexei A. Gaivoronski. Stochastic quasigradient methods for optimization of discrete event systems. Ann. Oper. Res., 39(1-4):1–39 (1993), 1992. [1088] Yu. M. Ermoljev and E.A. Nurminskiy. Stochastic quasigradient algorithms for minimax problems in stochastic programming. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 275–285. Academic Press, London, 1980. [1089] A.N. Ermolov. Revelation of preferences in a Bayesian game-theoretic model of social choice. Dokl. Akad. Nauk, 333(3):293–296, 1993. [1090] G. Escher. Sequentielle Zuordnungsprobleme. In Sechste Oberwolfach-Tagung uber¨ Operations Research (1973), Teil II, pages 1–13. Operations Research Verfahren, Band XIX, Hain, Miesen- heim am Glan, 1974. [1091] L. F. Escudero, C. Garcia, J. L. de la Fuente, and F. J. Prieto. Hydropower generation management under uncertainty via scenario analysis and parallel computation. IEEE Transactions on Power Systems, 11(2):683–689, 1996. [1092] L. F. Escudero, A. Garín, M. Merino, and G. Perez.´ A two-stage stochastic integer programming approach as a mixture of branch-and-fix coordination and Benders decomposition schemes. Ann. Oper. Res., 152:395–420, 2007. [1093] L. F. Escudero, I. Paradinas, and F. J. Prieto. Generation expansion planning under uncertainty in demand, economic environment, generation availability and book life. In Proceedings of the IEEE Stockholm Power Tech, pages 226–233, Stockholm, Sweden, 1995. [1094] L. F. Escudero, F. J. Quintana, and J. Salmeron. CORO, a modeling and an algorithmic framework for oil supply, transformation and distribution optimization under uncertainty. European Journal of Operational Research, 114(3):638–656, 1999. [1095] L. F. Escudero, J. Salmeron, I. Paradinas, and M. Sanchez. SEGEM: A simulation approach for electric generation management. IEEE Transactions on Power Systems, 13(3):738–748, 1998. [1096] Laureano F. Escudero, Araceli Garín, María Merino, and Gloria Perez.´ The value of the stochastic solution in multistage problems. TOP, 15(1):48–64, 2007. [1097] Laureano F. Escudero, Pasumarti V. Kamesam, Alan J. King, and Roger J.-B. Wets. Production planning via scenario modelling. Ann. Oper. Res., 43(1-4):311–335, 1993. Applied mathematical programming and modelling (Uxbridge, 1991). [1098] L.F. Escudero and P.V. Kamesam. On solving stochastic production planning problems via scenario modelling. Top, 3(1):69–95, 1995. [1099] Augustine O. Esogbue and Amar J. Singh. A stochastic model for an optimal priority bed distribution problem in a hospital ward. Operations Res. 24, 884-898, 1976.

62 [1100] Juan Estalrich and Nathan Buras. Alternative specifications of state variables in stochastic- dynamic-programming models of reservoir operation. Appl. Math. Comput., 44(2, part II):143– 155, 1991. [1101] Alexander Ettinger and Peter L. Hammer. Pseudo-Boolean programming with random coefficients. Cahiers Centre Etudes´ Recherche Oper.´ , 14:67–82, 1972. [1102] R. Everitt and W.T. Ziemba. Two-period stochastic programs with simple recourse. Oper. Res., 27(3):485–502, 1979. [1103] A. Evgrafov and M. Patriksson. On the existence of solutions to stochastic mathematical programs with equilibrium constraints. J. Optim. Theory Appl., 121(1):65–76, 2004. [1104] I. V. Evstigneev and M. I. Taksar. Convex stochastic optimization for random fields on graphs: a method of constructing Lagrange multipliers. Math. Methods Oper. Res., 54(2):217–237, 2001. [1105] Igor V. Evstigneev and Sjur D. Flam.˚ Convex stochastic duality and the “biting lemma”. J. Convex Anal., 9(1):237–244, 2002. [1106] Igor V. Evstigneev and Priscilla E. Greenwood. Stochastic extrema, splitting random elements and models of crack formation. In System modelling and optimization (Compiegne,` 1993), volume 197 of Lecture Notes in Control and Inform. Sci., pages 315–319. Springer, London, 1994. [1107] I.V. Evstigneev. Optimal stochastic programs and their stimulating prices. In Math. Models Econ., Proc. Sympos. math. Meth. Econ. and Conf. von Neumann Models, Warszawa 1972, 219-252, 1974. [1108] I.V. Evstigneev. Lagrange multipliers for the problems of stochastic programming. In Warsaw Fall Semin. math. Econ. 1975, Lect. Notes Econ. math. Syst. 133, 34-48, 1976. [1109] I.V. Evstigneev. Measurable selection and dynamic programming. Math. Oper. Res. 1, 267-272, 1976. [1110] I.V. Evstigneev. Turnpike theorems in stochastic models of economic dynamics. Mat. Zametki (Math. Notes) (translated into English), v.19, n.2, 279-290, 1976. [1111] I.V. Evstigneev. Homogeneous convex models in the theory of controlled random processes. Dok- lady AN SSSR (Soviet Math. Dokl.) (translated into English), v.253, n.3, 524-527, 1980. [1112] I.V. Evstigneev. Measurable selection theorems and stochastic control models in general topological spaces. Mat. Sbornik (Math. USSR Sbornik) (translated into English), v.131, n.1, 27-39, 1986. [1113] I.V. Evstigneev. Controlled random fields on a directed graph. Teor. Ver. i Primen. (Theory of Probab. and Appl.) (translated into English), v.33, n.3, 465-479, 1988. [1114] I.V. Evstigneev. Stochastic extremal problems and the strong Markov property of random fields. Uspekhi Matem. Nauk (Russian Math. Surveys) (translated into English), vol. 43, nr. 2, 3-41, 1988. [1115] I.V. Evstigneev. The shortest path around an island outside the shallows. Markov Processes and Related Fields, v.1, 407-418, 1995. [1116] I.V. Evstigneev and V.I. Arkin. Stochastic models of control and economic dynamics. Academic Press, London, 1987. [1117] I.V. Evstigneev and S.D. Flaam. The turnpike property and the central limit theorem in stochastic models of economic dynamics. In Yu.M. Kabanov, B.L. Rozovskii, and A.N. Shiryaev, editors, Statistics and Control of Stochastic Processes, pages 63–101. World Scientific, Singapore - New Jersey - London, 1997.

63 [1118] I.V. Evstigneev and P.E. Greenwood. Markov fields over countable partially ordered sets: Extrema and splitting. Memoirs of Amer. Math. Soc., v. 112 (537), 1994. [1119] I.V. Evstigneev and M.I. Taksar. Stochastic equilibria on graphs, I. Journal of Math. Economics, v. 23, 401-433, 1994. [1120] I.V. Evstigneev and M.I. Taksar. Stochastic equilibria on graphs, II. Journal of Math. Economics, v. 24, 383-406, 1995. [1121] James B. Ewbank, Bob L. Foote, and Hillel J. Kumin. A method for the solution of the distribution problem of stochastic linear programming. SIAM J. Appl. Math., 26:225–238, 1974. [1122] Eweda Eweda and Odile Macchi. Convergence of an adaptive linear estimation algorithm. IEEE Trans. Autom. Control AC-29, 119-127, 1984. [1123] I.¯ I.¯ E¯ zovˇ and Hoang Sum.ˇ Maximization processes with discrete time. Teor. Verojatnost. i Mat. Statist., 9:82–89, 175, 1973. [1124] B. A. Faber and J. R. Stedinger. Reservoir optimization using sampling sdp with ensemble streamflow prediction (esp) forecasts. Journal of Hydrology, 249(1–4):113–133, 2001. [1125] Malte Michael Faber. Stochastisches Programmieren. Wuerzburg-Wien: Physica-Verlag., 1970. [1126] C. Fabian and M. Stoica. Fuzzy integer programming. In Fuzzy sets and decision analysis, TIMS Stud. Manage. Sci. 20, 123-131 , 1984. [1127] Csaba I. Fabi´ an.´ Adapting an approximate level method to the two-stage stochastic programming problem. Stochastic Programming E-Print Series, http://www.speps.org, 2001. [1128] Csaba I. Fabian. Decomposing cvar minimization in two-stage stochastic models. Stochastic Programming E-Print Series, http://www.speps.org, 2005. [1129] Csaba I. Fabi´ an,´ Richard´ Nemedi,´ and Zoltan´ Szoke.˝ A stochastic programming model for optical fiber manufacturing. CEJOR Cent. Eur. J. Oper. Res., 9(4):343–359, 2001. [1130] Csaba I. Fabi´ an,´ Andras´ Prekopa,´ and Olga Ruf-Fiedler. On a dual method for a specially structured linear programming problem with application to stochastic programming. Optim. Methods Softw., 17(3):445–492, 2002. Stochastic programming. [1131] Csaba I. Fabian and Anna Veszpremi. Algorithms for handling cvar-constraints in dynamic stochastic programming models with applications to finance. Stochastic Programming E-Print Series, http://www.speps.org, 2007. [1132] V. Fabian. Simulated annealing simulated. Comput. Math. Appl., 33(1-2):81–94, 1997. Approxi- mation theory and applications. [1133] Vaclav Fabian. A local asymptotic minimax optimality of an adaptive Robbins-Monro stochastic approximation procedure. In Mathematical learning models - theory and algorithms, Proc. Conf., Bad Honnef/Ger. 1982, Lect. Notes Stat. 20, 43-49, 1983. [1134] Ulrich Faigle and Alexander Schoenhuth. Note on Negative Probabilities and Observable Pro- cesses. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl. de/05031, 2005. [1135] Ulrich Faigle and Rainer Schrader. On the convergence of stationary distributions in simulated annealing algorithms. Inf. Process. Lett. 27, No.4, 189-194, 1988. [1136] Shu-Kai S. Fan and Erwie Zahara. Stochastic response surface optimization via an enhanced Nelder-Mead simplex search procedure. Eng. Optim., 38(1):15–36, 2006.

64 [1137] Yu Bin Fan. The Bayesian statistical method for estimating the OD trip matrix from link volumes. Tongji Daxue Xuebao Ziran Kexue Ban, 19(2):227–233, 1991. [1138] Zhen Fan. Stochastic programming model with CVaR-recourse criterion for credit portfolio optimization. Comm. Appl. Math. Comput., 20(1):56–62, 2006. [1139] G. Fandel and J. Wilhelm. Rational solution principles and information requirements as elements of a theory of multiple criteria decision making. With a comment by P. Hansen. In Multiple Criteria Decis. Making, Proc. Conf. Jouy-en-Josas 1975, Lect. Notes Econ. Math. Syst. 130, 215-231, 1976. [1140] H. T. Fang and H. F. Chen. Almost surely convergent global optimization algorithm using noise- corrupted observations. J. Optim. Theory Appl., 104(2):343–376, 2000. [1141] Kai-Tai Fang, Dietmar Maringer, Yu Tang, and Peter Winker. Lower bounds and stochastic optimization algorithms for uniform designs with three or four levels. Math. Comp., 75(254):859–878 (electronic), 2006. [1142] Kai Tai Fang and Yuan Wang. A sequential algorithm for optimization and its applications to regression analysis. In Lecture notes in contemporary mathematics, 1989, pages 17–28. Science Press, Beijing, 1990. [1143] S.C. Fang and J.R. Rajasekera. Quadratically constrained minimum cross-entropy analysis. Math. Programming, 44(1 (Ser. A)):85–96, 1989. [1144] Weiwu Fang. On a global optimization problem in the study of information discrepancy. J. Global Optim., 11(4):387–408, 1997. [1145] Dan D. Farcas. On decomposability of some random automata with rewards. Stud. Cercet. Mat. 34, 9-18, 1982. [1146] Yahya Fathi. SQVAM: a variance minimizing algorithm. Oper. Res. Lett., 10(8):461–466, 1991. [1147] Gino Favero. Shortfall risk minimization under model uncertainty in the binomial case: adaptive and robust approaches. Math. Methods Oper. Res., 53(3):493–503, 2001. [1148] I.K. Fedorenko and V.I. Rymaruk. Some approaches to solving stochastic allocation problems. Issled. Operatsii i ASU, 26:3–6, 116, 1985. [1149] V.V. Fedorov. Stochastic decomposition in extremal problems. Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., 1:52–57, 73, 1980. [1150] A.N. Fedotov. An algorithm for the solution of a class of problems of stochastic programming. In Dynamics of non-homogeneous systems, Mater. Semin., Moskva 1983, 130-140 , 1983. [1151] A.V. Fedotov. An algorithm for the solution of M-problems of stochastic programming. In Methods of the investigation of complex systems, Proc. Conf., Moskva 1985, 30-35, 1985. [1152] Sergei Fedotov and Sergei Mikhailov. Option pricing for incomplete markets via stochastic optimization: transaction costs, adaptive control and forecast. Int. J. Theor. Appl. Finance, 4(1):179– 195, 2001. [1153] A.A. Fedulov, Yu.G. Fedulov, and V.N. Tsygichko. Introduction to the theory of statistically non- reliable solutions. (Vvedenie v teoriyu statisticheski nenadezhnykh reshenij). Moskva: ”Statistika”., 1979. [1154] E.A. Feinberg. Parametric stochastic dynamic programming. In Statistics and control of stochastic processes. Vol. 2, Pap. Steklov Semin., Moscow/USSR 1985-86, Transl. Ser. Math. Eng., 103-120, 1989.

65 [1155] Eugene A. Feinberg and Adam Shwartz, editors. Handbook of Markov decision processes, volume 40 of International Series in Operations Research & Management Science. Kluwer Academic Publishers, Boston, MA, 2002. Methods and applications. [1156] B. R. Feiring, T. Sastri, and L. S. M. Sim. A stochastic programming model for water resource planning. Mathematical and Computer Modelling, 27(3):1–7, 1998. [1157] L.I. Fejgin. Ein Zuordnungsproblem bei unvollstaendiger Information ueber die Gestehungskosten von Operationen. Izv. Akad. Nauk SSSR, Tekh. Kibern. 1970, No.6, 33-40, 1970. [1158] Sandor´ Fekete, Rolf Klein, and Andreas Nuchter.¨ Searching with an Autonomous Robot. In S. Al- bers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [1159] Paul Feldman and Silvio Micali. An optimal probabilistic algorithm for synchronous Byzantine agreement. In Automata, languages and programming, Proc. 16th Int. Colloq., Stresa/Italy 1989, Lect. Notes Comput. Sci. 372, 341-378, 1989. [1160] M. Fels, D.S. Lycon, D.J. Meeuwig, J.W. Meeuwig, and J.D. Pinter. An intelligent decision support system for assisting industrial wastewater management. Annals of Operations Research, 58:455– 477, 1995. [1161] En Min Feng, Guang Yan Shi, Gui Qing Gao, and Huan Wen Tan. Application of stochastic programming in the design and management of a special purpose wharf. Math. Practice Theory, 1:9–14, 1984. [1162] Yingjun Feng and Xuefeng Wang. Fuzzy convex programming. Fuzzy Math. 7, No.3/4, 23-26, 1987. [1163] Afonso G. Ferreira and Janez Zerovnik.ˇ Bounding the probability of success of stochastic methods for global optimization. Comput. Math. Appl., 25(10-11):1–8, 1993. [1164] Michael C. Ferris and Andrzej Ruszczynski.´ Robust path choice in networks with failures. Net- works, 35(3):181–194, 2000. [1165] Miroslav Fiedler. Doubly stochastic matrices and optimization. In Advances in mathematical optimization, Pap. Dedic. F. Nozicka Occas. 70. Birthday, Math. Res. 45, 44-51, 1988. [1166] Olga Fiedler and Werner Romisch.¨ Stability in multistage stochastic programming. Ann. Oper. Res., 56:79–93, 1995. Stochastic programming (Udine, 1992). [1167] S. Filippi and S. Czakay. Ein modifiziertes Hooke-Jeeves-Verfahren und ein modifiziertes Choit- Schrack-Verfahren zur nichtlinearen Optimierung. Math. Operationsforsch. Stat., Ser. Optimization 13, 419-429, 1982. [1168] Financial optimization. Physica-Verlag, Heidelberg, 1999. Math. Methods Oper. Res. 50 (1999), no. 2. [1169] Ulrich Fincke and Horst W. Hamacher. On the expected value of stochastic linear programs and (dynamic) network flow problems. European J. Oper. Res., 29(3):307–316, 1987. [1170] Charles H. Fine and Robert M. Freund. Optimal investment in product-flexible manufacturing capacity. Manage. Sci. 36, No.4, 449-466, 1990. [1171] P. Fischer and E.R. Swart. Three-dimensional line stochastic matrices and extreme points. Linear Algebra Appl., 69:179–203, 1985. [1172] I.H. Fisher. Derivation of optimal stocking policies for grazing in arid regions. I. Methodology. Appl. Math. Comput. 17, 1-35, 1985.

66 [1173] George S. Fishman and David S. Rubin. Bounding the variance in Monte Carlo experiments. Oper. Res. Lett., 11(4):243–248, 1992. [1174] Sjur D. Flaam and Alberto Seeger. Solving cone-constrained convex programs by differential inclusions. Math. Program. 65A, No.1, 107-121, 1994. [1175] S.D. Flam.˚ Nonanticipativity in stochastic programming. J. Optim. Theory Appl., 46(1):23–30, 1985. [1176] S.D. Flam and J.D. Pinter. Selecting oil exploration strategies: Some stochastic programming formulations and solution methods. Research Report CMI 852611-1, Christian Michelsen Institute, Fantoft, Bergen, Norway, 1985. [1177] S.D. Flam˚ and J. Zowe. Exact penalty functions in single-stage stochastic programming. Optimiza- tion, 21(5):723–734, 1990. [1178] Sjur D. Flam.˚ Asymptotically stable solutions to stochastic optimization problems. In Stochastic programming (Gargnano, 1983), volume 76 of Lecture Notes in Control and Inform. Sci., pages 184–193. Springer, Berlin, 1986. [1179] Sjur D. Flam.˚ Shadow prices in stochastic programming: their existence and significance. In Stochastic models and option values (Loen, 1989), volume 200 of Contrib. Econom. Anal., pages 227–240. North-Holland, Amsterdam, 1991. [1180] Sjur D. Flam. Finite convergence in stochastic programming. In Stochastic optimization. Numeri- cal methods and technical applications, Proc. GAMM/IFIP-Workshop, Neubiberg/Ger. 1990, Lect. Notes Econ. Math. Syst. 379, 1-14, 1992. [1181] Sjur D. Flam.˚ Lagrange multipliers in stochastic programming. SIAM J. Control Optim., 30(1):1– 10, 1992. [1182] Sjur D. Flam˚ and Rudiger¨ Schultz. A new approach to stochastic linear programming. Numer. Funct. Anal. Optim., 14(5-6):545–554, 1993. [1183] Sjur D. Flam˚ and Roger J.-B. Wets. Finite horizon approximates of infinite horizon stochastic programs. In Stochastic optimization (Kiev, 1984), volume 81 of Lecture Notes in Control and Inform. Sci., pages 339–350. Springer, Berlin, 1986. [1184] Sjur Didrik Flam.˚ Corrigendum: “Lagrange multipliers in stochastic programming” [SIAM J. Control. Optim. 30 (1992), no. 1, 1–10; MR 93c:90051]. SIAM J. Control Optim., 33(2):667–671, 1995. [1185] Sjur Didrik Flam.˚ Stochastic programming, cooperation, and risk exchange. Optim. Methods Softw., 17(3):493–504, 2002. Stochastic programming. [1186] Sjur Didrik Flam.˚ Optimization under uncertainty using momentum. In Dynamic stochastic optimization (Laxenburg, 2002), volume 532 of Lecture Notes in Econom. and Math. Systems, pages 249–256. Springer, Berlin, 2004. [1187] Lisa Fleischer, Jochen Konemann,¨ Stefano Leonardi, and Guido Schafer.¨ Simple cost sharing schemes for multicommodity rent-or-buy and stochastic Steiner tree. In STOC’06: Proceedings of the 38th Annual ACM Symposium on Theory of Computing, pages 663–670, New York, 2006. ACM. [1188] Stein-Erik Fleten, Kjetil Høyland, and Stein W. Wallace. The performance of stochastic dynamic and fixed mix portfolio models. European J. Oper. Res., 140(1):37–49, 2002. [1189] Stein-Erik Fleten and Trine Krogh Kristoffersen. Short-term hydropower production planning by stochastic programming. Stochastic Programming E-Print Series, http://www.speps.org, 2006.

67 [1190] Stein-Erik Fleten and Trine Krogh Kristoffersen. Stochastic programming for optimizing bidding strategies of a nordic hydropower producer. Stochastic Programming E-Print Series, http:// www.speps.org, 2006. [1191] Stein-Erik Fleten and Snorre Lindset. Optimal hedging strategies for multi-period guarantees in the presence of transaction costs: A stochastic programming approach. Stochastic Programming E-Print Series, http://www.speps.org, 2006. [1192] Stein-Erik Fleten and Erling Pettersen. Optimization of physical purchasing for a price-taking retailer in the norwegian electricity market. Stochastic Programming E-Print Series, http:// www.speps.org, 2005. [1193] Stein-Erik Fleten, Stein W. Wallace, and William T. Ziemba. Hedging electricity portfolios via stochastic programming. Stochastic Programming E-Print Series, http://www.speps.org, 1999. [1194] Stein-Erik Fleten, Stein W. Wallace, and William T. Ziemba. Hedging electricity portfolios via stochastic programming. In Decision making under uncertainty, volume 128 of IMA Vol. Math. Appl., pages 71–93. Springer, New York, 2002. [1195] C.J. Fodor and J.D. Pinter. Extreme order statistics applied for optimum estimation in ’hard’ MP problems. In Transactions of the Tenth Prague Conference on Information Theory, Statistical Decision Functions, and Random Processes. (Prague, July, 1986), pages 321–328, Prague, 1988. Publishing House of the Czechoslovakian Academy of Sciences. [1196] Janos´ C. Fodor and Janos´ Pinter.´ Extreme order statistics applied for optimum estimation in “hard” MP problems. In Transactions of the Tenth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, Vol. A (Prague, 1986), pages 321–328. Reidel, Dordrecht, 1988. [1197] Renato Fonso. On a stochastic transportation problem. In Proceedings of the First AMASES Meet- ing (Pisa, 1977) (Italian), pages 149–182, Turin, 1979. Giappichelli. [1198] Renato Fonso. On the convergence of a feasible directions algorithm for optimization problems with linear constraints and strictly convex non-differentiable objective function. Riv. Mat. Sci. Econ. Soc. 5, 115-122, 1982. [1199] B.L. Foote. A discussion of the properties of a basic simplex algorithm for generating the decision regions of Bereanu. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 207–222, London, 1980. Academic Press. [1200] Jean-Pierre Forestier. Optimisation de la commande des systemes a representation semi- markovi- enne. In Mathematiques appliquees, 1er Colloq. AFCET-SMF, Palaiseau 1978, Tome I, 337-346, 1978. [1201] O. B. Fosso, A. Gjelsvik, A. Haugstad, B. Mo, and I. Wangensteen. Generation scheduling in a deregulated system. The Norwegian case. IEEE Transactions on Power Systems, 14(1):75–80, 1999. [1202] Robert Fourer and Leo Lopes. A management system for decompositions in stochastic programming. Ann. Oper. Res., 142:99–118, 2006. [1203] Robert Fourer and Leo Lopes. StAMPL: A ﬁltration-oriented modeling tool for stochastic programming. Optimization Online, http://www.optimization-online.org, 2006. [1204] L. Fourgeaud and S. Fourgeaud. Critere de choix en avenir partiellement incertain. Rev. Franc. Inform. Rech. Oper. 2, No.14, 9-19, 1968.

68 [1205] E. Fragniere and A. Haurie. A stochastic programming model for energy/environment choices under uncertainty. International Journal of Environment and Pollution, 6(4–6):587–603, 1996. In Georghe, A. V. (ed), “Integrated Regional Health and Environmental Risk Assessment and Safety Management”. [1206] Emmanuel Fragniere` and Jacek Gondzio. Stochastic programming from modeling languages. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 95–113. SIAM, Philadelphia, PA, 2005. [1207] Emmanuel Fragniere,` Jacek Gondzio, and Jean-Philippe Vial. Building and solving large-scale stochastic programs on an affordable distributed computing system. Ann. Oper Res., 99:167–187 (2001), 2000. Applied mathematical programming and modeling, IV (Limassol, 1998). [1208] P. M. Franca and H. P. L. Luna. Solving stochastic transportation-location problems by generalized Benders decomposition. Transportation Science, 16(2):113–126, 1982. [1209] Linos F. Frantzeskakis and Warren B. Powell. A successive linear approximation procedure for stochastic, dynamic vehicle allocation problems. Transportation Sci., 24(1):40–57, 1990. [1210] Linos F. Frantzeskakis and Warren B. Powell. Bounding procedures for multistage stochastic dynamic networks. Networks, 23(7):575–595, 1993. [1211] Linos F. Frantzeskakis and Warren B. Powell. Restricted recourse strategies for bounding the expected network recourse function. Ann. Oper. Res., 64:261–287, 1996. Stochastic programming, algorithms and models (Lillehammer, 1994). [1212] Astrid Franz and Karl Heinz Hoffmann. Optimal annealing schedules for a modiﬁed Tsallis statistics. J. Comput. Phys., 176(1):196–204, 2002. [1213] K. Frauendorfer. Bounding the expectation of a function of a multivariate random variable— with application to stochastic programming. In XI symposium on operations research (Darmstadt, 1986), volume 57 of Methods Oper. Res., pages 13–23. Athenaum/Hain/Hanstein,¨ Konigstein/Ts.,¨ 1987. [1214] K. Frauendorfer. Solving SLP recourse problems: the case of stochastic technology matrix, RHS & objective. In System modelling and optimization (Tokyo, 1987), volume 113 of Lecture Notes in Control and Inform. Sci., pages 90–100. Springer, Berlin, 1988. [1215] K. Frauendorfer. Stochastic dynamic optimization: modelling and methodological aspects. In System modelling and optimization (Compiegne,` 1993), volume 197 of Lecture Notes in Control and Inform. Sci., pages 332–341. Springer, London, 1994. [1216] K. Frauendorfer and P. Kall. A solution method for SLP recourse problems with arbitrary multivariate distributions—the independent case. Problems Control Inform. Theory/Problemy Upravlen. Teor. Inform., 17(4):177–205, 1988. [1217] K. Frauendorfer and Ch. Marohn. Reﬁnement issues in stochastic multistage linear programming. In Stochastic programming methods and technical applications (Neubiberg/Munich, 1996), pages 305–328. Springer, Berlin, 1998. [1218] Karl Frauendorfer. Solving SLP recourse problems with arbitrary multivariate distributions—the dependent case. Math. Oper. Res., 13(3):377–394, 1988. [1219] Karl Frauendorfer. On the value of perfect information and approximate solutions in convex stochastic two-stage optimization. In System modelling and optimization (Zurich, 1991), volume 180 of Lecture Notes in Control and Inform. Sci., pages 564–573. Springer, Berlin, 1992. [1220] Karl Frauendorfer. Stochastic two-stage programming, volume 392 of Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin, 1992. Habilitationsschrift, University of Zurich,¨ Zurich,¨ 1992.

69 [1221] Karl Frauendorfer. The approximation of separable stochastic programs. J. Comput. Appl. Math., 56(1-2):23–44, 1994. Stochastic programming: stability, numerical methods and applications (Gosen, 1992). [1222] Karl Frauendorfer. Multistage stochastic programming: error analysis for the convex case. Z. Oper. Res., 39(1):93–122, 1994. [1223] Karl Frauendorfer. Barycentric scenario trees in convex multistage stochastic programming. Math. Programming, 75(2, Ser. B):277–293, 1996. Approximation and computation in stochastic programming. [1224] Karl Frauendorfer and Jens Gussow.¨ Stochastic multistage programming in the operation and management of a power system. In Stochastic optimization techniques (Neubiberg/Munich, 2000), volume 513 of Lecture Notes in Econom. and Math. Systems, pages 199–222. Springer, Berlin, 2002. [1225] Karl Frauendorfer and Gido Haarbrucker.¨ Test problems in stochastic multistage programming. Optimization, 47(3-4):267–285, 2000. Numerical methods for stochastic optimization and real- time control of robots (Neubiberg/Munich, 1998). [1226] Karl Frauendorfer and Michael Schurle.¨ Term structure models in multistage stochastic programming: estimation and approximation. Ann. Oper Res., 100:189–209 (2001), 2000. Research in stochastic programming (Vancouver, BC, 1998). [1227] James R. Freeland and Gerhard Schiefer. Using probabilistic information in solving resource allocation problems for a decentralized firm. Internat. J. Policy Anal. Inform. Systems, 5(4):325–340, 1981. [1228] P. Freeman and A.E. Gear. A probabilistic objective function for R P D portfolio selection. Operat. Res. Quart. 22, 253-265, 1971. [1229] Michael Freimer, Doug Thomas, and Jeff Linderoth. Reducing bias in stochastic linear programming with sampling methods. Optimization Online, http://www.optimization-online. org, 2005. [1230] J.B.G. Frenk, A.H.G. Rinnooy Kan, and L. Stougie. A hierarchical scheduling problem with a well-solvable second stage. Annals of Operations Research, 1:43–58, 1984. [1231] H. Frick. On the solution of the facility location problem when the dominance method fails. Z. Oper. Res., Ser. B 29, B101-B106, 1985. [1232] Bozenaˇ Friedrich and Klaus Tammer. Untersuchungen zur Stabilitat¨ einiger Ersatzprobleme der stochastischen Optimierung in Bezug auf anderungen¨ des zugrunde gelegten Zufallsvektors. Wiss. Z. Humboldt-Univ. Berlin Math.-Natur. Reihe, 30(5):373–376, 1981. [1233] A.M. Frieze. An algorithm for finding Hamilton cycles in random directed graphs. J. Algorithms 9, No.2, 181-204, 1988. [1234] Klaus Fritzsch. On the acceleration of adaptation processes by two-step principles. Kybernetika, Praha 13, 274-281, 1977. [1235] D.D. Frolkin. A stochastic problem of planning storage and irrigation. Zh. Vychisl. Mat. i Mat. Fiz., 21(3):595–604, 810, 1981. [1236] D.D. Frolkin. The solution of some stochastic two-stage problems. U.S.S.R. Comput. Math. Math. Phys. 24, No.3, 123-128 translation from Zh. Vychisl. Mat. Mat. Fiz. 24, No.6, 823-830 (1984)., 1984. [1237] E. Frostig and I. Adiri. Stochastic flowshop no-wait scheduling. J. Appl. Probab. 22, 240-246, 1985.

70 [1238] Bor-Ruey Fu. Modeling and analysis of discrete tandem production lines using continuous flow models. Ph.D. Dissertation, Department of Industrial Engineering, University of Wisconsin– Madison, Madison, WI, 1996. [1239] M.C. Fu. Convergence of a stochastic approximation algorithm for the GI/G/1 queue using infinitesimal perturbation analysis. J. Optimization Theory Appl. 65, No.1, 149-160, 1990. [1240] M.C. Fu and S.D. Hill. Optimization of discrete event systems via simultaneous perturbation stochastic approximation. Transactions of the Institute of Industrial Engineers, 29:233–243, 1997. [1241] Michael C. Fu. Optimization via simulation: a review. Ann. Oper. Res., 53:199–247, 1994. Simu- lation and modeling. [1242] Toshiharu Fujita and Kazuyoshi Tsurusaki. Optimizing the expectation of negative multiplicative functions. Surikaisekikenky¯ usho¯ Koky¯ uroku¯ , 978:160–172, 1997. Optimization methods for mathematical systems with uncertainty (Japanese) (Kyoto, 1996). [1243] Toshiharu Fujita and Kazuyoshi Tsurusaki. Stochastic optimization of multiplicative functions with negative value. J. Oper. Res. Soc. Japan, 41(3):351–373, 1998. [1244] Hiroshi Fujiwara and Kazuo Iwama. Average-Case Competitive Analyses for Ski-Rental Problems. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algo- rithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [1245] Takeshi Fukao and Tetsuya Harada. Decomposition of objective function in stochastic combinatorial optimization. In System modelling and optimization (Leipzig, 1989), volume 143 of Lecture Notes in Control and Inform. Sci., pages 599–610. Springer, Berlin, 1990. [1246] Kazuma Fukuda, Hitoshi Hagiwara, and Mario Nakamori. Analysis of probabilistic algorithms for the knapsack problem. Surikaisekikenky¯ usho¯ Koky¯ uroku¯ , 947:162–171, 1996. Optimization theory in mathematical models (Japanese) (Kyoto, 1995). [1247] Masao Fukushima. A fixed point approach to certain convex programs with applications in stochastic programming. Math. Oper. Res. 8, 517-524, 1983. [1248] Nagata Furukawa. Recurrence set-relations in stochastic multiobjective dynamic decision processes. Math. Operationsforsch. Stat., Ser. Optimization 13, 113-121, 1982. [1249] R.I. Furunziev and A.Ja. Ismailov. Eine experimentelle Untersuchung von Algorithmen der stochastischen Optimierung dynamischer Systeme. Wiss. Z. Techn. Hochschule Ilmenau 25, No.1, 173-180, 1979. [1250] A. Futschik and G. Pflug. Confidence sets for discrete stochastic optimization. Ann. Oper. Res., 56:95–108, 1995. Stochastic programming (Udine, 1992). [1251] R. Gabasov and V.G. Medvedev. An algorithm for solving a two-stage linear stochastic programming problem with several random parameters. Dokl. Akad. Nauk BSSR, 32(1):13–16, 92, 1988. [1252] J. M. Gablonsky and C. T. Kelley. A locally-biased form of the DIRECT algorithm. J. Global Optim., 21(1):27–37, 2001. [1253] Manal Gabour, Simeon Reich, and Alexander J. Zaslavski. Generic convergence of algorithms for solving stochastic feasibility problems. In Inherently parallel algorithms in feasibility and optimization and their applications (Haifa, 2000), volume 8 of Stud. Comput. Math., pages 279– 295. North-Holland, Amsterdam, 2001. [1254] Norman Gaither. An experimental solution of the general stochastic programming problem. Simu- lation 30, 191-195, 1978.

71 [1255] V.G. Gaitsgori and A.A. Pervozvanskii. Approximate optimality of sliding planning. Automat. Remote Control, 38(10, part 2):1505–1511 (1978), 1977. [1256] A. Gaivoronski. Linearization methods for optimization of functionals which depend on probability measures. Math. Programming Stud., 28:157–181, 1986. Stochastic programming 84. II. [1257] A. Gaivoronski. Stochastic optimization techniques for finding optimal submeasures. In Stochastic optimization (Kiev, 1984), volume 81 of Lecture Notes in Control and Inform. Sci., pages 351–363. Springer, Berlin, 1986. [1258] A. Gaivoronski. Numerical techniques for finding estimates which minimize the upper bound of the absolute deviation. In Statistical data analysis based on the L1-norm and related methods (Neuch sp atel, 1987), pages 247–262, Amsterdam, 1987. North-Holland. [1259] A. Gaivoronski. Stochastic quasigradient methods and their implementation. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 313–351. Springer, Berlin, 1988. [1260] A. Gaivoronski, E. Messina, and A. Sciomachen. A stochastic optimization approach for robot scheduling. Ann. Oper. Res., 56:109–133, 1995. Stochastic programming (Udine, 1992). [1261] A.A. Gaivoronski and E. Messina. Stochastic optimization algorithms for regenerative DEDS. In System modelling and optimization (Compiegne,` 1993), volume 197 of Lecture Notes in Control and Inform. Sci., pages 320–331. Springer, London, 1994. [1262] A.A. Gaivoronski, E. Messina, and A. Sciomachen. A statistical generalized programming algorithm for stochastic optimization problems. Ann. Oper. Res., 58:297–321, 1995. Applied mathematical programming and modeling, II (APMOD 93) (Budapest, 1993). [1263] Alexei A. Gaivoronski. A numerical method for solving stochastic programming problems with moment constraints on a distribution function. Ann. Oper. Res., 31(1-4):347–369, 1991. Stochastic programming, Part II (Ann Arbor, MI, 1989). [1264] Alexei A. Gaivoronski. SQG: software for solving stochastic programming problems with stochastic quasi-gradient methods. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 37–60. SIAM, Philadelphia, PA, 2005. [1265] Alexei A. Gaivoronski. Stochastic optimization problems in telecommunications. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 669–704. SIAM, Philadel- phia, PA, 2005. [1266] Alexei A. Gaivoronski and Petter E. de Lange. An asset liability management model for casualty insurers: complexity reduction vs. parameterized decision rules. Ann. Oper Res., 99:227–250 (2001), 2000. Applied mathematical programming and modeling, IV (Limassol, 1998). [1267] Alexei A. Gaivoronski, Kjetil Høyland, and Petter E. de Lange. Statutory regulation of casualty insurance companies: an example from Norway with stochastic programming analysis. In Stochas- tic optimization: algorithms and applications (Gainesville, FL, 2000), volume 54 of Appl. Optim., pages 55–85. Kluwer Acad. Publ., Dordrecht, 2001. [1268] Alexei A. Gaivoronski and Fabio Stella. Stochastic nonstationary optimization for finding universal portfolios. Ann. Oper Res., 100:165–188 (2001), 2000. Research in stochastic programming (Vancouver, BC, 1998). [1269] A.A. Gaivoronskii. Some methods for the solution of a nonstationary stochastic programming problem with constraints. In Methods of operations research and of reliability theory in systems analysis (Russian), pages 70–79, Kiev, 1977. Akad. Nauk. Ukrain. SSR Inst. Kibernet.

72 [1270] A.A. Gaivoronskii. Identification approach to problems of stochastic programming with independent tests. In Mathematical methods in operations research and reliability theory (Russian), pages 87–91, Kiev, 1978. Akad. Nauk Ukrain. SSR Inst. Kibernet. [1271] A.A. Gaivoronskii. A nonstationary stochastic programming problem with changing constraints. In Mathematical methods in operations research and reliability theory (Russian), pages 24–30. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1978. [1272] A.A. Gaivoronskii. Nonstationary stochastic programming problems. Kibernetika (Kiev), 4:89–92, 1978. [1273] A.A. Gaivoronskii. Approximation methods of solution of stochastic programming problems. Cy- bernetics, 18(2):241–249, 1982. [1274] A.A. Gaivoronskii. Numerical methods for minimizing convex functionals from probability measures with applications to optimal monitoring. Kibernetika (Kiev), 4:43–51, 134, 1989. [1275] A.A. Gaivoronskii. A numerical method for searching for optimal submeasures. Kibernetika (Kiev), 2:70–77, 136, 1990. [1276] A.A. Gaivoronskii and Le Din’ Fung. Solution of nonstationary and limit stochastic inequalities. Issled. Operatsii i ASU, 13:98–104, 135, 1979. [1277] A.A. Gajvoronskij. Methods of search of optimal sets. Cybernetics 14, 731-735 translation from Kibernetika 1978, No.5, 83-86 (1978)., 1979. [1278] A.A. Gajvoronskij. Numerical minimization methods for convex functionals dependent on probability measures with applications to optimal pollution monitoring. Cybernetics 25, No.4, 471-482 translation from Kibernetika 1989, No.4, 43-51 (1989)., 1989. [1279] A.A. Gajvoronskij. A numerical method to find optimal submeasures. Cybernetics 26, No.2, 234- 246 translation from Kibernetika 1990, No.2, 70-77 (1990)., 1990. [1280] A.D. Gajvoronskij and Yu.M. Ermol’ev. Methods of finding optimal submeasures (characterization of solutions). Cybernetics 23, No.5, 684-694 translation from Kibernetika 1987, No.5, 94-101 (1987)., 1987. [1281] Alexei A. Gajvoronskij. Optimization of stochastic discrete event dynamic systems: A survey of some recent results. In Simulation and optimization, Proc. Int. Workshop Comput. Intensive Methods Simulation Optimization, Laxenburg/Austria 1990, Lect. Notes Econ. Math. Syst. 374, 24-44, 1992. [1282] Shmuel Gal and Charles A. Micchelli. Optimal sequential and nonsequential procedures for eval- uating a functional. Applicable Anal., 10(2):105–120, 1980. [1283] Tomas Gal, editor. Grundlagen des Operations Research. 3: Spieltheorie, Dynamische Opti- mierung, Lagerhaltung, Warteschlangentheorie, Simulation, Unscharfe Entscheidungen. Mit Beitr. von M. J. Beckmann, H. Gehring, K.-P. Kistner, Ch. Schneeweiss, G. Schwoediauer, H.-J. Zimmer- mann. Springer-Verlag, 1987. [1284] Tomas Gal and Hartmut Wolf. Solving stochastic linear programs via goal programming. In Decision making with multiple objectives (Cleveland, Ohio, 1984), volume 242 of Lecture Notes in Econom. and Math. Systems, pages 126–143. Springer, Berlin, 1985. [1285] Giulia Galbiati. On the asymptotic probabilistic analysis of scheduling problems in the presence of precedence constraints. J. Complexity 6, No.2, 149-165, 1990. [1286] E. A. Galperin and N. M. Yanev. One-dimensional analogue of the global optimization. C. R. Acad. Bulgare Sci., 53(5):29–32, 2000.

73 [1287] Wolf Gamerith. Ueber gemischte unscharfe Ansaetze zum multi-criteria-Problem. Methods Oper. Res. 43, 63-71, 1981. [1288] R.V. Gamkrelidze, editor. Progress in mathematics. Vol. 11: Probability theory, mathematical statistics, and theoretical cybernetics. Translated from Russian by J. S. Wood. New York-London: Plenum Press., 1971. [1289] M.S. Gamze. A method for the parametrization of one-step problems of operative linear stochastic programming. Kibernetika (Kiev), 1:71–74, 79, 135, 1988. [1290] Cheng Yun Gao. Efficient equilibria and the core in a stochastic market. Qufu Shifan Daxue Xuebao Ziran Kexue Ban, 21(5):119–122, 1995. [1291] Cheng Yun Gao. Optimal selection for stochastic continuous location on closed convex sets. Qufu Shifan Daxue Xuebao Ziran Kexue Ban, 22(2):15–19, 1996. [1292] Linchun Gao and Andras´ Prekopa.´ Lower and upper bounds for the probability that at least r and exactly r out of n events occur. Math. Inequal. Appl., 5(2):315–333, 2002. [1293] Alfredo Garcia and Robert L. Smith. Solving nonstationary infinite horizon stochastic production planning problems. Oper. Res. Lett., 27(3):135–141, 2000. [1294] I. Garcia and G.T. Herman. Global optimization by parallel constrained biased random search. In State of the art in global optimization (Princeton, NJ, 1995), volume 7 of Nonconvex Optim. Appl., pages 433–455. Kluwer Acad. Publ., Dordrecht, 1996. [1295] J.-M. Garcia and A. Turgeon. Gestion optimale d’un ensemble hydro-electrique: Aspects long terme et court terme. RAIRO, Autom. Syst. Anal. Control 15, 243-262, 1981. [1296] M. a Pilar García-Carrasco Aponte. Some cases of optimal allocation of observations. Trabajos Estadist.´ Investigacion´ Oper., 30(2):3–31, 1979. [1297] D. T. Gardner. Flexibility in electric power planning: Coping with demand uncertainty. Energy, 21(2):1207–1218, 1996. [1298] D. T. Gardner and J. S. Rogers. Planning electric power systems under demand uncertainty with different technology lead times. Management Science, 45:1289–1306, 1999. [1299] L.E. Garey and R.D. Gupta. A note on continuous search algorithms. J. Appl. Probab., 24(1):277– 280, 1987. [1300] N.I. Garkusha. Investigation of the adaptive properties of production-transportation systems by means of stochastic models. Issled. Operatsii i ASU, 35:11–20, 1991. [1301] Izaskun Garrido and Marc C. Steinbach. A multistage stochastic programming approach in real- time process control. In Online optimization of large scale systems, pages 479–498. Springer, Berlin, 2001. [1302] Stanley J. Garstka. Stochastic programs with recourse: random recourse costs only. Management Sci., 19:747–750, 1972/73. [1303] Stanley J. Garstka. Regularity conditions for a class of convex programs. Management Sci., Theory 20, 373-377, 1973. [1304] Stanley J. Garstka. Distribution functions in stochastic programs with recourse: a parametric analysis. Math. Programming, 6:339–351, 1974. [1305] Stanley J. Garstka. On duality in stochastic programming with recourse. Z. Wahrscheinlichkeits- theorie und Verw. Gebiete, 29:21–24, 1974.

74 [1306] Stanley J. Garstka. The economic equivalence of several stochastic programming models. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 83–91, London, 1980. Academic Press. [1307] Stanley J. Garstka. An economic interpretation of stochastic programs. Math. Programming, 18(1):62–67, 1980. [1308] Stanley J. Garstka and David P. Rutenberg. Computation in discrete stochastic programs with recourse. Operations Res., 21:112–122, 1973. Mathematical programming and its applications. [1309] Stanley J. Garstka and Roger J.-B. Wets. On decision rules in stochastic programming. Math. Programming, 7:117–143, 1974. [1310] Bernd Gartner¨ and Emo Welzl. Linear programming—randomization and abstract frameworks. In STACS 96 (Grenoble, 1996), volume 1046 of Lecture Notes in Comput. Sci., pages 669–687, Berlin, 1996. Springer. [1311] H. Gassmann. Conditional probability and conditional expectation of a random vector. In Nu- merical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 237–254. Springer, Berlin, 1988. [1312] H. Gassmann. MSLIP, a computer code for the multistage stochastic linear programming problem. Mathematical Programming, 47:407–423, 1990. [1313] H. Gassmann and W.T. Ziemba. A tight upper bound for the expectation of a convex function of a multivariate random variable. Math. Programming Stud., 27:39–53, 1986. Stochastic programming 84. I. [1314] H. I. Gassmann and Andras´ Prekopa.´ On stages and consistency checks in stochastic programming. Oper. Res. Lett., 33(2):171–175, 2005. [1315] H. I. Gassmann and E. Schweitzer. A comprehensive input format for stochastic linear programs. Ann. Oper Res., 104:89–125 (2002), 2001. Modeling languages and systems. [1316] H.I. Gassmann and A.M. Ireland. On the formulation of stochastic linear programs using algebraic modelling languages. Ann. Oper. Res., 64:83–112, 1996. Stochastic programming, algorithms and models (Lillehammer, 1994). [1317] H.I. Gassmann and J.D. Pinter. Modelling tools for stochastic programs. Working Paper 97-1, School of Business Administration, Dalhousie University, Halifax, 1997. [1318] Horand I. Gassmann. The SMPS format for stochastic linear programs. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 9–19. SIAM, Philadelphia, PA, 2005. [1319] Horand I. Gassmann and David M. Gay. An integrated modeling environment for stochastic programming. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 159–175. SIAM, Philadelphia, PA, 2005. [1320] Horand I. Gassmann, Sandra L. Schwartz, Stein W. Wallace, and William T. Ziemba. Introduction to stochastic programming applications. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 179–184. SIAM, Philadelphia, PA, 2005. [1321] Horand I. Gassmann and Stein W. Wallace. Solving linear programs with multiple right-hand sides: pricing and ordering schemes. Ann. Oper. Res., 64:237–259, 1996. Stochastic programming, algorithms and models (Lillehammer, 1994). [1322] Horand I. Gassmann, Stein W. Wallace, and William T. Ziemba. Stochastic programming computer implementations. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 3–8. SIAM, Philadelphia, PA, 2005.

75 [1323] W. Gaul. On stochastic analysis of project-networks. In Deterministic and stochastic scheduling, Proc. NATO Adv. Study Res. Inst., Durham/Engl. 1981, 297-309, 1982. [1324] W. Gaul. Financial planning via stochastic programming: a stochastic ﬂows-with-gains approach. In Risk and capital (Ulm, 1983), volume 227 of Lecture Notes in Econom. and Math. Systems, pages 181–197. Springer, Berlin, 1984. [1325] Wolfgang Gaul. Bounds for the expected duration of a stochastic project planning model. J. Inform. Optim. Sci., 2(1):45–63, 1981. [1326] Wolfgang Gaul. Stochastische Projektplanung und Marketingprobleme. Methods Oper. Res. 44, 539-552, 1981. [1327] Wolfgang Gaul. Marketing-Logistik bei stochastischer Nachfrage. In Operations research, Proc. 11th Annu. Meet., Frankfurt a.M. 1982, 73-80 , 1983. [1328] Carlo Gavarini. Applications de la programmation mathematique a l’analyse limite des structures. Revue Franc. Automat. Inform. Rech. operat. 7, V-3, 55-68, 1973. [1329] T. Gavin. Etudes numeriques et applications de processus d’approximation stochastique. Ann. sci. Univ. Clermont 58, Math. 12, 94-109, 1976. [1330] Andrzej Gawrych-Zukowski. Some problems of multi-objective programming with fuzzy constraints. Syst. Sci. 7, 75-86, 1981. [1331] A.A. Gayvoronskiy and Yu. M. Yermol’yev. Problems of stochastic programming with subsequent estimation of the parameters. Engrg. Cybernetics, 17(4):22–31 (1980), 1979. [1332] H.P. Geering and M. Mansour(ed.). Large scale systems; theory and applications 1986. Selected papers from the 4th IFAC/IFORS Symposium, Zuerich, Switzerland, August 26-29, 1986. Volume 2. IFAC Proceedings Series, 1987, No.11. International Federation of Automatic Control. Oxford etc.: Pergamon Press. XV, 396 p., ISBN 0-08- 034084-9, 1987. [1333] S. Geetha and K.P.K. Nair. A stochastic bottleneck transportation problem. J. Oper. Res. Soc. 45, No.5, 583-588, 1994. [1334] William V. Gehrlein and Peter C. Fishburn. Information overload in mechanical processes. Man- agement Sci. 23, 391-398, 1976. [1335] Robert Geist and Robert Reynolds. The most likely steady state for large numbers of stochastic traveling salesman. In Numerical solution of Markov chains, volume 8 of Probab. Pure Appl., pages 529–541. Dekker, New York, 1991. [1336] Saul B. Gelfand and Sanjoy K. Mitter. Recursive stochastic algorithms for global optimization in rd . SIAM J. Control Optim., 29(5):999–1018, 1991. [1337] S.B. Gelfand and S.K. Mitter. Weak convergence of Markov chain sampling methods and annealing algorithms to diffusions. J. Optim. Theory Appl., 68(3):483–498, 1991. [1338] Mitsuo Gen and Baoding Liu. Evolution algorithm for optimal capacity expansion. J. Oper. Res. Soc. Japan, 40(1):1–9, 1997. [1339] Ian P. Gent, Ewan MacIntyre, Patrick Prosser, Barbara M. Smith, and Toby Walsh. Random constraint satisfaction: ﬂaws and structure. Constraints, 6(4):345–372, 2001. [1340] Yigal Gerchak and Mordechai Henig. An inventory model with component commonality. Oper. Res. Lett. 5, 157-160, 1986. [1341] L. Gerencser. The application of a stochastic Broyden method in the self-tuning control of a heat- pump. Z. Angew. Math. Mech. 63, No.5, T408-T410, 1983.

76 [1342] L. Gerencser. Convergence of a stochastic variable metric method with application in adaptive prediction. In System modelling and optimization, Proc. 11th IFIP Conf., Copenhagen 1983, Lect. Notes Control Inf. Sci. 59, 443-450, 1984. [1343] L. Gerencser.´ Strong consistency theorems related to stochastic quasi-Newton methods. In Stochas- tic optimization (Kiev, 1984), volume 81 of Lecture Notes in Control and Inform. Sci., pages 364– 372. Springer, Berlin, 1986. [1344] L. Gerencser.´ Rate of convergence of moments of Spall’s SPSA method. In Stochastic Differential and Difference Equations, Series on Progress in Systems and Control Theory, volume 23, pages 67–75. Birkhauser,¨ Boston, 1997. [1345] L. Gerencser.´ Convergence rate of moments in stochastic approximation with simultaneous perturbation gradient approximation and resetting. IEEE Transactions on Automatic Control, 44:894– 905, 1999. [1346] L. Gerencser,´ S.D. Hill, and Z. Vag´ o.´ Optimization over discrete sets using SPSA. In Proceedings of the IEEE Conference on Decision and Control, pages 1791–1795, 1999. [1347] L. Gerencser´ and Z. Vag´ o.´ SPSA in noise-free optimization. In Proceedings of the American Control Conference, pages 3284–3288, 2000. [1348] Laszl´ o´ Gerencser´ and Zsuzsanna Vag´ o.´ Non-smooth optimization with randomization. In Op- timization theory (Matrah´ aza,´ 1999), volume 59 of Appl. Optim., pages 111–117. Kluwer Acad. Publ., Dordrecht, 2001. [1349] Laszl´ o´ Gerencser,´ Zsuzsanna Vag´ o,´ and H. Hjalmarsson. Randomization methods in optimization and adaptive control. In Stochastic theory and control (Lawrence, KS, 2001), volume 280 of Lecture Notes in Control and Inform. Sci., pages 137–153. Springer, Berlin, 2002. [1350] Allen Gersho. Adaptive ﬁltering with binary reinforcement. IEEE Trans. Inf. Theory IT-30, 191- 199, 1984. [1351] Dieter Geuting and Klaus Hellwig. Einige Bemerkungen zum Zweistuﬁgen Stochastischen Pro- grammieren. In Operations Research Verfahren XXIV, Symp. Mannheim 1978, 57-59, 1977. [1352] Horst-Dieter Geuting. Entscheidungen unter Ungewissheit. Loesungsansaetze der stochastischen Programmierung bei endlichem Zustandsraum., 1978. [1353] Charles J. Geyer. On the asymptotics of constrained M-estimation. Ann. Statist., 22(4):1993–2010, 1994. [1354] G.Gurkan.¨ Simulation optimization of buffer allocations in production lines with unreliable machines. Annals of Operations Research, 93:177–216, 2000. [1355] G.Gurkan,¨ A.Y. Ozge,¨ and S.M. Robinson. Sample-path solutions for simulation optimization problems and stochastic variational inequalities. In D.L. Woodruff, editor, Advances in Compu- tational and Stochastic Optimization, Logic Programming, and Heuristic Search: Interfaces in Computer Science and Operations Research, pages 169–188, Boston, 1998. Kluwer Academic Publishers. [1356] G.Gurkan,¨ A.Y. Ozge,¨ and S.M. Robinson. Solving stochastic optimization problems with stochastic constraints: An application in network design. In P.A. Farrington, H.B. Nembhard, D.T. Stur- rock, and G.W. Evans, editors, Proceedings of the 1999 Winter Simulation Conference, pages 471– 478, 1999. [1357] Saied Ghannadan and Stein W. Wallace. Feasibility in uncapacitated networks: the effect of individual arcs and nodes. Ann. Oper. Res., 64:197–210, 1996. Stochastic programming, algorithms and models (Lillehammer, 1994).

77 [1358] G. Giappichelli, editor. Atti del Primo Convegno A.M.A.S.E.S., Pisa, November 4-5, 1977., 1979. Torino: VIII, 393 p. L 10.000.00. [1359] Basilis Gidas. Simulations and global optimization. In Random media, IMA Vol. Math. Appl. 7, 129-145, 1987. [1360] A.B. Gil’, A.I. Kaplinskii, and V. M. Umyvakin. Information base of procedures for searching for optimal variants of an object that does not use differential characteristics of the quality exponent. In Optimization and modeling in automated systems (Russian), pages 4–10. Voronezh. Politekhn. Inst., Voronezh, 1988. [1361] E.` Kh. Gimadi. Justiﬁcation of a priori estimates for the quality of the approximate solution of a standardization problem. Upravlyaemye Sistemy, 27:12–27, 88–89, 1987. [1362] M.Ja. Ginzburg and M.I. Burtman. Ueber die operative Ressourcenverteilung auf grossen zweit- eiligen Transportnetzen ohne Zyklen. Ekonom. i Mat. Metody 13, 302-310, 1977. [1363] V.L. G¯irko. Limit theorems for the solutions of systems of linear random equations and the eigen- values and determinants of random matrices. Dokl. Akad. Nauk SSSR, 212:1039–1042, 1973. [1364] V.L. Girko and V.V. Smirnova. Asimptoticheskie metody resheniya nekotorykh zadach lineinogo stokhasticheskogo programmirovaniya i modelei tipa zatraty-vypusk, volume 83 of Preprint. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1983. [1365] V.L. Girko and V.V. Smirnova. Method of integral representations for the solution of problems of linear stochastic programming. Kibernetika 1983, No.6, 122-124, 1983. [1366] Vyacheslav L. Girko. Integral representation and resolvent methods for solving of linear stochastic programming problems of large dimensions. In System modelling and optimization (Zurich, 1991), volume 180 of Lecture Notes in Control and Inform. Sci., pages 574–579. Springer, Berlin, 1992. [1367] M.B. Gitman, P.V. Trusov, and S.A. Fedoseev. On the stochastic optimization problems of plastic metal-working processes. J. Math. Sci. (New York), 84(3):1109–1112, 1997. [1368] Michael B. Gitman, Peter V. Trusov, and Sergei A. Fedoseev. On the stochastic optimization problems of plastic metal working processes under stochastic initial conditions. Korean J. Comput. Appl. Math., 6(1):111–125, 1999. [1369] J.C. Gittins. Resource allocation in speculative chemical research. J. appl. Probab. 11, 255-265, 1974. [1370] K.D. Glazebrook. On non-preemptive strategies for stochastic scheduling problems in continuous time. Int. J. Syst. Sci. 12, 771-782, 1981. [1371] K.D. Glazebrook. Decomposable jump decision processes. Stochastic Processes Appl. 13, 333- 334, 1982. [1372] K.D. Glazebrook. On a sufﬁcient condition for superprocesses due to Whittle. J. Appl. Probab. 19, 99-110, 1982. [1373] K.D. Glazebrook, R.J. Boys, and N.A. Fay. On the evaluation of strategies for branching bandit processes. Ann. Oper. Res. 30, 299-319, 1991. [1374] Kevin D. Glazebrook. Semi-Markov models for single-machine stochastic scheduling problems. Int. J. Syst. Sci. 16, 573-587, 1985. [1375] Alan Gleit. Statistical decision theory and linear programming. The non-constrained case., 1977. [1376] Alan Gleit. Stochastic linear programming. Matematisk Institut, Aarhus Universitet, Aarhus, 1977. Lecture Notes Series, No. 49.

78 [1377] I.A. Glinkin. On the search for global extrema of functions which are representable in the form of an integral on a domain of variable configuration. Vopr. Kibern., Mosk. 122, 91-97, 1985. [1378] I.A. Glinkin. Search for the global extremum of functions represented as an integral over a domain of variable configuration. Voprosy Kibernet. (Moscow), 122:91–97, 1985. [1379] B.M. Glover, B.D. Craven, and S.D. Flam. A generalized Karush-Kuhn-Tucker optimality condition without constraint qualification using the approximate subdifferential. Numer. Funct. Anal. Optimization 14, No.3-4, 333-353, 1993. [1380] V.M. Gluskov and G.B. Olejars. Einige Probleme der stochastischen Programmierung, die in Dialogsystemen der Planung unter den Verhaeltnissen unvollstaendiger Informationen entstehen. Kibernetika, Kiev 1977, No.3, 100-104, 1977. [1381] O.V. Gluskova.ˇ Finite-difference methods for solving stochastic minimax problems. Dokl. Akad. Nauk Ukrain. SSR Ser. A, 10:78–81, 96, 1980. [1382] V.A. Gnatjuk. An algorithm for the simultaneous solution of the direct and the dual problems of convex programming in a Banach space. Kibernetika (Kiev), 1:102–107, 1975. [1383] Willy Gochet. A note on the E-model of chance-constrained programming with random b- vector. Management Sci., Theory 21, 844-845, 1975. [1384] Willy F. Gochet and Manfred W. Padberg. The triangular E-model of chance-constrained programming with stochastic A-matrix. Management Sci., 20:1284–1291, 1973/74. [1385] A.F. Godonoga. Some properties in problems of quadratic stochastic programming. Mat. Issled., 82:24–29, 152, 1985. Mat. Modeli Met. Optim. [1386] A.F. Godonoga. Stochastic schemes for finding the minimax. Mat. Issled., 116:3–13, 96, 1990. Veroyatnost. i Prilozhen. [1387] C.D. Godsil. Tools from linear algebra. In Handbook of combinatorics, Vol. 1, 2, pages 1705–1748. Elsevier, Amsterdam, 1995. With an appendix by L. Lovasz.´ [1388] Vikas Goel and Ignacio E. Grossmann. A class of stochastic programs with decision dependent uncertainty. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [1389] Vikas Goel and Ignacio E. Grossmann. A class of stochastic programs with decision dependent uncertainty. Math. Program., 108(2-3, Ser. B):355–394, 2006. [1390] A.S. Gofmark. Stochastic programming problems with penalty estimates when the coefficients of the matrix A are random. Taskent.ˇ Inst. Narod. Hoz. Naucn.ˇ Zap., 34:68–76, 1970. Mat. v Prilozen. [1391] A.S. Gofmark. Stochastic programming problems with probabilistic constraints when the coefficients of the matrix A are random. Taskent.ˇ Inst. Narod. Hoz. Naucn.ˇ Zap., 34:77–87, 1970. Mat. v Prilozen. [1392] C.J. Goh and K.L. Teo. On constrained stochastic optimal parameter selection problems. Bull. Austral. Math. Soc., 41(3):393–405, 1990. [1393] Ambrose Goicoechea and Lucien Duckstein. Nonnormal deterministic equivalents and a transformation in stochastic mathematical programming. Appl. Math. Comput., 21(1):51–72, 1987. [1394] K. Gokbayrak and C. G. Cassandras. Online surrogate problem methodology for stochastic discrete resource allocation problems. J. Optim. Theory Appl., 108(2):349–376, 2001. [1395] K. Gokbayrak and C. G. Cassandras. Generalized surrogate problem methodology for online stochastic discrete optimization. J. Optim. Theory Appl., 114(1):97–132, 2002.

79 [1396] Bruce L. Golden, Arjang A. Assad, and Stelios H. Zanakis. Statistics and optimization: the interface. Amer. J. Math. Management Sci., 4(1-2):1–5, 1984. Statistics and optimization : the interface. [1397] Thomas Goll and Jan Kallsen. Optimal portfolios for logarithmic utility. Stochastic Process. Appl., 89(1):31–48, 2000. [1398] R. Gollmer, M. P. Nowak, W. Romisch,¨ and R. Schultz. Unit commitment in power generation—a basic model and some extensions. Annals of Operations Research, 96:167–189, 2000. [1399] Ralf Gollmer, Uwe Gotzes, and Rudiger¨ Schultz. Second-order stochastic dominance constraints induced by mixed-integer linear recourse. Stochastic Programming E-Print Series, http://www. speps.org, 2007. [1400] Ralf Gollmer, Frederike Neise, and Rudiger¨ Schultz. Stochastic programs with first-order dominance constraints induced by mixed-integer linear recourse. Stochastic Programming E-Print Se- ries, http://www.speps.org, 2007. [1401] Alexandr N. Golodnikov, Pavel S. Knopov, Panos M. Pardalos, and Stanislav P. Uryasev. Optimiza- tion in the space of distribution functions and applications in the Bayes analysis. In Probabilistic constrained optimization, volume 49 of Nonconvex Optim. Appl., pages 102–131. Kluwer Acad. Publ., Dordrecht, 2000. [1402] A.N. Golodnikov. Search for the extremum of a linear functional in a class of distribution functions satisfying linear constraints of the inequality type. Akad. Nauk Ukrain. SSR Inst. Kibernet. Preprint, 13:7–14, 53, 1979. Stochastic optimization models. [1403] A.N. Golodnikov. A method of solving certain stochastic problems with partially defined distribution function. Engrg. Cybernetics, 18(2):14–20 (1981), 1980. [1404] A.N. Golodnikov, Yu.M. Ermol’ev, and Ts.Kh. Nedeva. Problems of stochastic programming with unknown distribution functions. Izv. Akad. Nauk SSSR, Tekh. Kibern. 1983, No.3, 180-188, 1983. [1405] B. Golub, M. Holmer, R. McKendall, L. Pohlman, and S.A. Zenios. Stochastic programming models for money management. European Journal of Operations Research, 85:282–296, 1995. [1406] Luiz F.A.M. Gomes. On modelling equilibrium traffic flow assignment with elastic demand as a stochastic nonlinear vector optimization problem. Found. Control Eng. 11, 157-166, 1986. [1407] Amilcar S. Goncalves. On the convexity of sets of parameters in parametric linear programming. Univ. Lisboa, Revista Fac. Ci., II. Ser., A 14, 61-78, 1972. [1408] J. Gondzio and A. Ruszczynski.´ Sensitivity method for basis inverse representation in multistage stochastic linear programming problems. J. Optim. Theory Appl., 74(2):221–242, 1992. [1409] Jacek Gondzio. Simplex modifications exploiting special features of dynamic and stochastic dynamic linear programming problems. Control Cybernet., 17(4):337–349 (1989), 1988. [1410] Jacek Gondzio and Roy Kouwenberg. High performance computing for asset liability management. Report MS-99-004, Econometric Institute, Erasmus University Rotterdam, The Netherlands, 1999. Available at http://mail.tinbinst.nl/˜kouwenbe/ms99004.ps. [1411] Jacek Gondzio and Andrzej Ruszczynski.´ A sensitivity method for solving multistage stochastic linear programming problems. In Aspiration based decision support systems, volume 331 of Lecture Notes in Econom. and Math. Systems, pages 68–79. Springer, Berlin, 1989. [1412] Linguo Gong. Chance-constrained linear programming with location scale distributions. Nav. Res. Logist. 39, No.7, 997-1007, 1992. [1413] Wei-Bo Gong, Yu-Chi Ho, and Wengang Zhai. Stochastic comparison algorithm for discrete optimization with estimation. SIAM J. Optim., 10(2):384–404 (electronic), 2000.

80 [1414] Graham C. Goodwin, David J. Hill, and Xie Xianya. Stochastic adaptive control for exponentially convergent time-varying systems. SIAM J. Control Optimization 24, 589-603, 1986. [1415] V.M. Gorbachuk. Stability of solutions of stochastic extremal problems. In Mathematical methods for the analysis of complex stochastic systems (Russian), pages 71–76, vi. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1988. [1416] Steven M. Gorelick. Large scale nonlinear deterministic and stochastic optimization: Formulations involving simulation of subsurface contamination. Math. Program., Ser. B 48, No.1, 19-39, 1990. [1417] B. G. Gorenstin, N. M. Campodonico,´ J. P. Costa, and M. V. F. Pereira. Stochastic optimization of a hydrothermal system including network constraints. IEEE Transactions on Power Systems, 7(2):791–797, 1992. [1418] B. G. Gorenstin, N. M. Campodonico,´ J. P. Costa, M. V. F. Pereira, and N. Deeb. Power-system expansion planning under uncertainty. IEEE Transactions on Power Systems, 8(1):129–136, 1993. [1419] A. Gorka and M. Kostreva. Probabilistic version of the method of feasible directions. Appl. Math. Comput., 130(2-3):253–264, 2002. [1420] S. Yu. Gorodetskii. Convergence and asymptotic estimates of behavior for a class of search methods. Dinamika Sistem, Dinam. Uprav.:140–163, 195, 1984. [1421] S.Yu. Gorodetskij and Yu.I. Nejmark. On the search characteristics of the algorithm of global optimization with an adaptive stochastic model. Probl. Sluchajnogo Poiska 9, 83-105, 1981. [1422] H.W. Gottinger. Stochastic decomposition of hierarchical systems. Angew. Inf. 18, 13-22, 1976. [1423] Uwe Gotzes. Optimal investments in distributed generation units under uncertainty. In CTW2006— Cologne-Twente Workshop on Graphs and Combinatorial Optimization, volume 25 of Electron. Notes Discrete Math., page 65 (electronic). Elsevier, Amsterdam, 2006. [1424] A. Gouda, D. Monhor, and T. Szantai.´ Stochastic programming based PERT modeling. In Coping with uncertainty, volume 581 of Lecture Notes in Econom. and Math. Systems, pages 241–255. Springer, Berlin, 2006. [1425] A. Gouda and T. Szantai.´ A new, stochastic programming model of PERT. Alkalmaz. Mat. Lapok, 22(1):97–113, 2005. [1426] John Goutsias and Jerry M. Mendel. Optimal simultaneous detection and estimation of ﬁltered discrete semi- Markov chains. IEEE Trans. Inf. Theory IT-34, No.3, 551-568, 1988. [1427] A.K. Govil and S. Kumar. Stochastic behaviour of a complex system under priority repair. Com- puting 6, 200-213, 1970. [1428] Alicja Grabowska. Randomness of a restriction vector in linear programming. Przeglk ad Statyst., 18:345–352, 1971. [1429] O.N. Granichin. Estimation of the minimum point of an unknown function observed against the background of dependent noise. Problemy Peredachi Informatsii, 28(2):16–20, 1992. [1430] V.I. Gricenko and N.A. Nazarenko. Problem of on-line control of multiphase supply systems. Kibernetika, Kiev 1978, No.2, 100-103, 1978. [1431] M.J. Grimble. Convergence of explicit LQG self-tuning controllers. IEE Proc., Part D 135, No.4, 309-322, 1988. [1432] S.N. Grincenko and L.A. Rastrigin. On matrix random search. Avtomat. vycislit. Tehn., Riga 1977, No.1, 48-51, 1977.

81 [1433] Richard C. Grinold. A new approach to multistage stochastic linear programs. Math. Programming Stud., 6:19–29, 1976. Stochastic systems: modeling, identification and optimization, II (Proc. Sympos., Univ. Kentucky, Lexington, Ky., 1975). [1434] Richard C. Grinold. Infinite horizon stochastic programs. SIAM J. Control Optim., 24(6):1246– 1260, 1986. [1435] P. J. F. Groenen, W. J. Heiser, and J. J. Meulman. Global optimization in least-squares multidimensional scaling by distance smoothing. J. Classification, 16(2):225–254, 1999. [1436] Luuk Groenewegen and Jaap Wessels. Conditions for optimality in multistage stochastic programming problems. In Recent results in stochastic programming (Proc. Meeting, Oberwolfach, 1979), volume 179 of Lecture Notes in Econom. and Math. Systems, pages 41–57. Springer, Berlin, 1980. [1437] Nicole Groewe and Werner Roemisch. A stochastic programming model for optimal power dispatch: Stability and numerical treatment. In Stochastic optimization. Numerical methods and technical applications, Proc. GAMM/IFIP-Workshop, Neubiberg/Ger. 1990, Lect. Notes Econ. Math. Syst. 379, 111-139, 1992. [1438] M.A. Grove. A surrogate for linear programs with random requirements. Eur. J. Oper. Res. 34, No.3, 399-402, 1988. [1439] Nicole Growe,¨ Werner Romisch,¨ and Rudiger¨ Schultz. A simple recourse model for power dispatch under uncertain demand. Ann. Oper. Res., 59:135–164, 1995. Models for planning under uncertainty. [1440] N. Growe-Kuska,¨ K. C. Kiwiel, M. P. Nowak, W. Romisch,¨ and I. Wegner. Power management in a hydro-thermal system under uncertainty by Lagrangian relaxation. In C. Greengard and A. Ruszczynski,´ editors, Decision Making under Uncertainty: Energy and Power, volume 128 of IMA volumes on Mathematics and its Applications, pages 39–70. Springer-Verlag, 2002. [1441] N. Growe-Kuska,¨ K.C. Kiwiel, M.P. Nowak, W. Romisch,¨ and I. Wegner. Power management under uncertainty by lagrangian relaxation. In Proceedings of the 6th International Conference Probabilistic Methods Applied to Power Systems (PMAPS 2000), volume 2, INESC Porto, 2000. [1442] Viviane Grunert da Fonseca, Carlos M. Fonseca, and Andreia O. Hall. Inferential performance assessment of stochastic optimisers and the attainment function. In Evolutionary multi-criterion optimization (Zurich, 2001), volume 1993 of Lecture Notes in Comput. Sci., pages 213–225. Springer, Berlin, 2001. [1443] Fu Wen Gu. Density estimation of measurable optimal value functions and measurable solutions in stochastic programming. J. Chengdu Univ. Sci. Tech., 2:143–146, 1987. [1444] Fu Wen Gu. Existence of optimal solutions for probabilistic constrained linear programming problems. J. Math. Res. Exposition, 15(2):293–296, 1995. [1445] Fu Wen Gu. An approximation method for a class of constrained probabilistic programs and its convergence. Sichuan Daxue Xuebao, 34(4):399–405, 1997. [1446] Fuwen Gu. Estimating the density function of optimal value function and measurable solution of stochastic programming. J. Chengdu Univ. Sci. Technol. 1987, No.2, 143-146, 1987. [1447] Jun Gu. Randomized and deterministic local search for SAT and scheduling problems. In Ran- domization methods in algorithm design (Princeton, NJ, 1997), pages 61–108. Amer. Math. Soc., Providence, RI, 1999. [1448] S. Guan and S.-C. Fang. Linear programming with stochastic elements: an on-line approach. Comput. Math. Appl., 33(9):61–82, 1997.

82 [1449] Sichong Guan and Shu-Cherng Fang. A global-filtering algorithm for linear programming problems with stochastic elements. Math. Methods Oper. Res., 48(3):287–316, 1998. [1450] Yongpei Guan, Shabbir Ahmed, and George L. Nemhauser. A branch-and-cut algorithm for the stochastic uncapacitated lot-sizing problem. Stochastic Programming E-Print Series, http:// www.speps.org, 2004. [1451] Yongpei Guan, Shabbir Ahmed, and George L. Nemhauser. Cutting planes for multi-stage stochastic integer programs. Stochastic Programming E-Print Series, http://www.speps.org, 2006. [1452] Yongpei Guan, Shabbir Ahmed, George L. Nemhauser, and Andrew J. Miller. A branch-and-cut algorithm for the stochastic uncapacitated lot-sizing problem. Math. Program., 105(1, Ser. A):55– 84, 2006. [1453] Yongpei Guan and Andrew Miller. Polynomial time algorithms for stochastic uncapacitated lot- sizing problems. Optimization Online, http://www.optimization-online.org, 2006. [1454] J. Guddat, W. Roemisch, and R. Schultz. Some applications of mathematical programming techniques in optimal power dispatch. Computing 49, No.3, 193-200, 1992. [1455] Juergen Guddat, Francisco Guerra Vasquez, Klaus Tammer, and Klaus Wendler. Multiobjective and stochastic optimization based on parametric optimization. Mathematical Research, 26. Berlin: Akademie-Verlag., 1985. [1456] Herbert Guelicher. Nichtlineares Programmieren unter stochastischen Nebenbedingungen. Eine Untersuchung im Verkehrssektor., 1964. [1457] Franco Guerriero and John Miltenburg. The stochastic U-line balancing problem. Naval Res. Logist., 50(1):31–57, 2003. [1458] Roger Guesnerie. Sur l’usage de la notion de probabilites´ subjectives. Rev. Française Automat. Informat. Recherche Operationnelle´ , 6(Ser. V-1):31–46, 1972. [1459] Harvey S. Gunderson, James G. Morris, and Howard E. Thompson. Stochastic programming with recourse: A modification from an applications viewpoint. J. Oper. Res. Soc. 29, 769-778, 1978. [1460] Xin Guo and Larry Shepp. Option pricing in a world with arbitrage. In Stochastic optimization: algorithms and applications (Gainesville, FL, 2000), volume 54 of Appl. Optim., pages 87–96. Kluwer Acad. Publ., Dordrecht, 2001. [1461] A.M. Gupal. A certain stochastic programming problem with constraints of a probabilistic nature. Kibernetika (Kiev), 6:94–100, 1974. [1462] A.M. Gupal. Eine Optimierungsmethode mit nichtstationaeren Restriktionen. Kibernetika, Kiev 1974, Nr. 3, 131-133, 1974. [1463] A.M. Gupal. A method of optimization under nonstationary conditions. Kibernetika (Kiev), 3:131– 133, 1974. [1464] A.M. Gupal. Ueber ein Problem der stochastischen Programmierung mit Beschraenkungen von wahrscheinlichkeitstheoretischer Natur. Kibernetika, Kiev 1974, Nr. 6, 94-100, 1974. [1465] A.M. Gupal. A method for the solution of stochastic programming problems. In Methods of operations research and reliability theory in systems analysis (Russian), pages 97–105, Kiev, 1976. Akad. Nauk Ukrain. SSR Inst. Kibernet. [1466] A.M. Gupal. Direct method of solution of stochastic programming problems. Automat. Remote Control, 38(4, part 1):502–506, 1977.

83 [1467] A.M. Gupal. Algorithms for the random search of an extremum of non-differentiable functions. Probl. Sluchajnogo Poiska 6, 121-129, 1978. [1468] A.M. Gupal. A method of solving stochastic problems with constraints of a probabilistic nature. Engrg. Cybernetics, 17(1):26–31 (1980), 1979. [1469] A.M. Gupal. Stochastic Methods for Solving Nonsmooth Extremal Problems. Naukova Dumka, Kiev, 1979. (in Russian). [1470] A.M. Gupal. Stochastic methods of minimization of nondifferentiable functions. Autom. Remote Control 40, 529-534 translation from Avtom. Telemekh. 1979, No.4, 61-66 (1979)., 1979. [1471] A.M. Gupal and L.G. Bazenov.ˇ A stochastic analogue of the conjugate gradient method. Kiber- netika (Kiev), 1:125–126, 1972. [1472] A.M. Gupal and L.G. Bazenov.ˇ A stochastic linearization method. Kibernetika (Kiev), 3:116–117, 1972. [1473] A.M. Gupal and V.B. Dubrovskii. Finite-difference Arrow-Hurwicz method with averaging. Kiber- netika (Kiev), 4:iv, 120–122, 136, 1985. [1474] A.M. Gupal and F. Mirzoahmedov. A way of regulating the step in stochastic programming methods. Kibernetika (Kiev), 1:133–134, 1978. [1475] Anupam Gupta, Martin Pal,´ Ramamoorthi Ravi, and Amitabh Sinha. What about Wednesday? Approximation algorithms for multistage stochastic optimization. In Approximation, randomization and combinatorial optimization, volume 3624 of Lecture Notes in Comput. Sci., pages 86–98. Springer, Berlin, 2005. [1476] Anupam Gupta, R. Ravi, and Amitabh Sinha. LP rounding approximation algorithms for stochastic network design. Math. Oper. Res., 32(2):345–364, 2007. [1477] N.K. Gupta. Direct search computational methods for maximum likelihood parameter estimation. In Proc. 1978 IEEE Conf. on decision and control, incl. 17th Symp. on adaptive processes, San Diego/Calif. 1979, 921-922, 1979. [1478] P.K. Gupta and Man Mohan. Linear programming and theory of games. 3rd extensively rev. ed. Tracts in Operations Research. New Delhi: Sultan Chand & Sons, Publishers., 1981. [1479] P.K. Gupta and Rakesh Kumar Verma. Optimal resource allocation in a complex queueing system. Math. Operationsforsch. Stat., Ser. Optimization 11, 507-512, 1980. [1480] Sandipan Gupta and M. Chakraborty. Stochastic fuzzy mathematical programming and decision. J. Fuzzy Math., 6(3):637–647, 1998. [1481] S.N. Gupta and A.K. Jain. Optimization with the ratio of independent normal variates. Acta Cienc. Indica Math., 12(3):209–212, 1986. [1482] S.N. Gupta, A.K. Jain, and Kanti Swarup. Stochastic linear fractional programming with the ratio of independent Cauchy variates. Naval Res. Logist., 34(2):293–305, 1987. [1483] S.N. Gupta and Rajeev Kumar Jain. Stochastic fractional programming under chance constraints with random technology matrix. Acta Cienc. Indica Math., 12(3):191–198, 1986. [1484] S.N. Gupta and Kanti Swarup. Note on stochastic programming for minimization of variance. New Zealand Oper. Res., 8(2):185–187, 1980. [1485] S.N. Gupta, Kanti Swarup, and Banwarilal. Stochastic fractional programming under chance constraints with random technology matrix. Gujarat Statist. Rev., 8(1):23–34, 1981.

84 [1486] G. Gurkan.¨ Performance Optimization in Simulation: Sample-Path Optimization of Buffer Allo- cations in Tandem Lines. Ph.D. Dissertation, Department of Industrial Engineering, University of Wisconsin–Madison, Madison, WI, 1996. [1487] Gul¨ Gurkan,¨ A. Yonca Ozge,¨ and Stephen M. Robinson. Sample-path solution of stochastic variational inequalities. Math. Program., 84(2, Ser. A):313–333, 1999. [1488] O.V. Guseva. On convergence of the random search method. Kibernetika, Kiev 1971, No.6, 143- 145, 1971. [1489] O.V. Guseva. Random minimization without computation of derivatives. Kibernetika (Kiev), 1:117–120, 1974. [1490] Walter J. Gutjahr and Georg Ch. Pflug. Simulated annealing for noisy cost functions. J. Global Optim., 8(1):1–13, 1996. [1491] Knut Haase. Lotsizing and scheduling for production planning. Lecture Notes in Economics and Mathematical Systems 408. Springer-Verlag, 1994. [1492] K. Hagglof. The implementation of the stochastic branch and bound method for applications in river basin water quality management. IIASA Working Paper WP-96-89, Laxenburg, Austria, 1996. [1493] A. Hahnewald-Busch and V. Nollau. An approximation procedure for stochastic dynamic programming in countable state space. Math. Operationsforsch. Stat., Ser. Optimization 9, 109-117, 1978. [1494] Bruce Hajek. Optimization by simulated annealing: a necessary and sufficient condition for convergence. In Adaptive statistical procedures and related topics (Upton, N.Y., 1985), volume 8 of IMS Lecture Notes—Monograph Ser., pages 417–427. Inst. Math. Statist., Hayward, Calif., 1986. [1495] Bruce Hajek. Cooling schedules for optimal annealing. Math. Oper. Res. 13, No.2, 311-329, 1988. [1496] Sylvia Halasz. On a stochastic programming problem with random coefficients. In Prog. Oper. Res., Eger 1974, Colloq. Math. Soc. Janos Bolyai 12, 493-498 , 1976. [1497] Keshava P. Halemane and Ignacio E. Grossmann. A remark on the paper: “Theoretical and computational aspects of the optimal design centering, tolerancing, and tuning problem” [IEEE Trans. Circuits and Systems 26 (1979), no. 9, 795–813; MR 80h:94045] by E. Polak and A. Sangiovanni- Vincentelli. IEEE Trans. Circuits and Systems, 28(2):163–164, 1981. [1498] S. Hamadene and J.-P. Lepeltier. Zero-sum stochastic differential games and backward equations. Systems Control Lett., 24(4):259–263, 1995. [1499] Saïd Hamadene and Jean-Pierre Lepeltier. Points d’equilibre´ dans les jeux stochastiques de somme non nulle. C.R. Acad. Sci. Paris Ser.´ I Math., 318(3):251–256, 1994. [1500] Alexandru Hampu. Duality for multiobjective stochastic programming. Gen. Math., 9(1-2):15–22, 2001. [1501] Alexandru Hampu. A stochastic programming model: the problem of minimum-risk with simple recourse. Int. J. Comput. Numer. Anal. Appl., 2(3):273–281, 2002. [1502] Kum Sun Han and Ryong Sop Jang. A theoretical consideration of stochastic improper linear programming. Su-hak, 4:21–23, 1994. [1503] Gary Handler. Termination policies for a two-state stochastic process. Naval Res. Logist. Quart. 19, 281-292, 1972. [1504] Pierre Hansen, Brigitte Jaumard, Marcus Poggi de Aragao,˜ Fabien Chauny, and Sylvain Perron. Probabilistic satisfiability with imprecise probabilities. Internat. J. Approx. Reason., 24(2-3):171– 189, 2000. Reasoning with imprecise probabilities (Ghent, 1999).

85 [1505] Behram Hansotia. Some special cases of stochastic programs with recourse. Operations Res., 25(2):361–363, 1977. [1506] Behram J. Hansotia. Stochastic linear programs with simple recourse: the equivalent deterministic convex program for the normal, exponential, and Erlang cases. Naval Res. Logist. Quart., 27(2):257–272, 1980. [1507] J. Harband. The existence of monotonic solutions of a nonlinear car-following equation. J. Math. Anal. Appl., 57(2):257–272, 1977. [1508] Jr. Harris, Frederick C. A stochastic optimization algorithm for Steiner minimal trees. In Proceed- ings of the Twenty-fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1994), volume 105, pages 54–64, 1994. [1509] William E. Hart. Sequential stopping rules for random optimization methods with applications to multistart local search. SIAM J. Optim., 9(1):270–290 (electronic), 1999. [1510] Peter R. Hartley. Value function approximation in the presence of uncertainty and inequality constraints. An application to the demand for credit cards. J. Econom. Dynam. Control, 20(1-3):63–92, 1996. [1511] R. Hartley. Inequalities in completely convex stochastic programming. J. Math. Anal. Appl., 75(2):373–384, 1980. [1512] Charles M. Harvey. Stochastic programming models for decreasing risk aversion. J. Oper. Res. Soc., 32(10):885–889, 1981. [1513] Kurt Hassig.¨ Stochastische lineare Programmierung und ihre Anwendungsmoglichkeiten¨ in der Wirtschaft. Hochschule St. Gallen, St. Gallen, 1971. Dissertation der Hochschule St. Gallen fur¨ Wirtschafts- und Sozialwissenschaften zur Erlangung der Wurde¨ eines Doktors der Wirtschaftswis- senschaften, Dissertation No. 399. [1514] K. K. Haugen. A stochastic dynamic programming model for scheduling of offshore petroleum fields with resource uncertainty. European Journal of Operational Research, 88:88–100, 1993. [1515] Kjetil K. Haugen, Arne Løkketangen, and David L. Woodruff. Progressive hedging as a meta- heuristic applied to stochastic lot-sizing. European J. Oper. Res., 132(1):116–122, 2001. [1516] Kjetil K. Haugen and Stein W. Wallace. Stochastic programming: potential hazards when random variables reflect market interaction. Ann. Oper. Res., 142:119–127, 2006. [1517] D. Haugland, A. Hallefjord, and H. Asheim. Models for petroleum field exploitation. European Journal of Operational Research, 37(1):58–72, 1988. [1518] Dag Haugland and Stein W. Wallace. Solving many linear programs that differ only in the righthand side. European J. Oper. Res., 37(3):318–324, 1988. [1519] H. Hauptmann. A statistic for judging solutions of the travelling salesman problem. In IX. Ober- wolfach Conference on Operations Research (Oberwolfach, 1978), volume 36 of Operations Res. Verfahren, pages 61–71. Hain, Konigstein/Ts.,¨ 1980. [1520] A. Haurie, Y. Smeers, and G. Zaccour. Toward a contract portfolio management model for a gas producing firm. INFOR, 30(3):257–273, 1992. [1521] A. Haurie, G. Zaccour, and Y. Smeers. Stochastic equilibrium programming for dynamic oligopolistic markets. J. Optim. Theory Appl., 66(2):243–253, 1990. [1522] Alain Haurie and Pierre L’Ecuyer. Approximation and bounds in discrete event dynamic programming. IEEE Trans. Autom. Control AC-31, 227-235, 1986.

86 [1523] Alain Haurie and Francesco Moresino. Computation of S-adapted equilibria in piecewise deterministic games via stochastic programming methods. In Advances in dynamic games and applications (Maastricht, 1998), pages 225–252. Birkhauser¨ Boston, Boston, MA, 2001. [1524] Kelly J. Hayhurst and Douglas R. Shier. A factoring approach for the stochastic shortest path problem. Oper. Res. Lett., 10(6):329–334, 1991. [1525] Zhi Yong He and Chong Chao Huang. Genetic algorithm based on simulation for two-stage stochastic programming. J. Math. (Wuhan), 24(6):690–694, 2004. [1526] Bernd Heidergott. A weak derivative approach to optimization of threshold parameters in a multicomponent maintenance system. J. Appl. Probab., 38(2):386–406, 2001. [1527] T. Heikkinen and A. Prekopa.´ Optimal power control in a wireless network using a model with stochastic link coefﬁcients. Naval Res. Logist., 52(2):178–192, 2005. [1528] W.-R. Heilmann. Solving a dynamic program by linear programming - general state and action spaces. In Proc. Oper. Res. 7, Vortr. Jahrestag. DGOR, Kiel 1977, 31-38, 1978. [1529] W.-R. Heilmann. Solving stochastic dynamic programming problems by linear programming—an annotated bibliography. Z. Operations Res. Ser. A-B, 22(1):A43–A53, 1978. [1530] Wolf-Rudiger¨ Heilmann. Linear programming of dynamic programs with unbounded rewards. In Operations Research Verfahren, XXIV, pages 94–105, Meisenheim, 1977. Hain. [1531] Wolf-Rudiger¨ Heilmann. Optimal selectors for stochastic linear programs. Appl. Math. Optim., 4(2):139–142, 1977/78. [1532] Wolf-Rudiger¨ Heilmann. Generalized linear programming of ﬁnite-stage dynamic programs. In Second Symposium on Operations Research (Rheinisch-Westfalische¨ Tech. Hochsch. Aachen, Aachen, 1977), Teil 1, Operations Res. Verfahren, XXVIII, pages 153–167. Hain, Konigstein/Ts.,¨ 1978. [1533] Wolf-Rudiger¨ Heilmann. A note on sequential minimax rules for stochastic linear programs. In Recent results in stochastic programming (Proc. Meeting, Oberwolfach, 1979), volume 179 of Lecture Notes in Econom. and Math. Systems, pages 59–65. Springer, Berlin, 1980. [1534] Wolf-Rudiger¨ Heilmann. A note on chance-constrained programming. J. Oper. Res. Soc., 34(6):533–537, 1983. [1535] Wolf-Ruediger Heilmann. Stochastische dynamische Optimierung als Spezialfall linearer Opti- mierung in halbgeordneten Vektorraeumen. Manuscr. Math. 23, 57-66, 1977. [1536] Wolf-Ruediger Heilmann. A linear programming approach to general non-stationary dynamic programming problems. Math. Operationsforsch. Stat., Ser. Optimization 10, 325-333, 1979. [1537] Wolf-Ruediger Heilmann. Solving multistage stochastic linear programming problems by nonstationary dynamic programming. Oper. Res. Verfahren 33, 173-184, 1979. [1538] Wolf-Ruediger Heilmann. Approximations and error bounds for multistage stochastic linear programs. Part 2: Approximation by a ”larger” model. Methods Oper. Res. 37, 349-356, 1980. [1539] Wolf-Ruediger Heilmann. A mathematical programming approach to Strassen’s theorem on distributions with given marginals. Math. Operationsforsch. Stat., Ser. Optimization 12, 593-596, 1981. [1540] Stanislaw Heilpern. Selected problems in the theory of fuzzy sets. Mat. Stos. (3), 16:27–38 (1981), 1980.

87 [1541] Thomas Heinze. An algorithm for multistage stochastic integer programs. In CTW2006—Cologne- Twente Workshop on Graphs and Combinatorial Optimization, volume 25 of Electron. Notes Dis- crete Math., page 69 (electronic). Elsevier, Amsterdam, 2006. [1542] Thomas Heinze and Rudiger¨ Schultz. A branch-and-bound method for multistage stochastic integer programs with risk objectives. Stochastic Programming E-Print Series, http://www.speps. org, 2007. [1543] H. Heitsch, W. Romisch,¨ and C. Strugarek. Stability of multistage stochastic programs. SIAM J. Optim., 17(2):511–525 (electronic), 2006. [1544] Holger Heitsch and Werner Romisch.¨ Scenario tree modelling for multistage stochastic programs. Stochastic Programming E-Print Series, http://www.speps.org, 2006. [1545] Holger Heitsch, Werner Romisch,¨ and Cyrille Strugarek. Stability of multistage stochastic programs. Stochastic Programming E-Print Series, http://www.speps.org, 2005. [1546] Michael Heitzer and Manfred Staat. Limit and shakedown analysis with uncertain data. In Stochas- tic optimization techniques (Neubiberg/Munich, 2000), volume 513 of Lecture Notes in Econom. and Math. Systems, pages 253–267. Springer, Berlin, 2002. [1547] Thorkell Helgason and Stein W. Wallace. Approximate scenario solutions in the progressive hedging algorithm. A numerical study with an application to ﬁsheries management. Ann. Oper. Res., 31(1-4):425–444, 1991. Stochastic programming, Part II (Ann Arbor, MI, 1989). [1548] G. Hellwig, P. Kall, and P. Abel, editors. Statistical Methods for Decission Processes. Daimler Benz AG, Stuttgart-Mohringen,¨ 1994. [1549] K. Hellwig and J. Huelsmann. Ueber ein Modell der Investitionsprogrammplanung unter Unsicher- heit. In Oper. Res. Verf. 18, VI. Oberwolfach-Tag. Oper. Res. 1973, 141-146, 1974. [1550] Raymond Hemmecke and Rudiger¨ Schultz. Decomposition methods for two-stage stochastic integer programs. In Online optimization of large scale systems, pages 601–622. Springer, Berlin, 2001. [1551] Raymond Hemmecke and Rudiger¨ Schultz. Decomposition of test sets in stochastic integer programming. Stochastic Programming E-Print Series, http://www.speps.org, 2001. [1552] A.L. Hempenius. A note on the relationship between the feasible regions of several types of chance constraints. Statistica Neerlandica, 27:185–186, 1973. [1553] P. Henaff.´ Hedging exotic derivatives through stochastic optimization. J. Econom. Dynam. Control, 22(8-9):1453–1466, 1998. Algorithms and economic dynamics (Geneva, 1996). [1554] Alena Henclova. Notes on free lunch in the limit and pricing by conjugate duality theory. Stochastic Programming E-Print Series, http://www.speps.org, 2005. [1555] Eligius M. T. Hendrix and Olivier Klepper. On uniform covering, adaptive random search and raspberries. J. Global Optim., 18(2):143–163, 2000. [1556] Eligius M. T. Hendrix, P. M. Ortigosa, and I. Garc´ia. On success rates for controlled random search. J. Global Optim., 21(3):239–263, 2001. International Workshop on Global Optimization, Part 3 (Florence, 1999). [1557] R. Henrion. On the connectedness of probabilistic constraint sets. J. Optim. Theory Appl., 112(3):657–663, 2002. [1558] Rene´ Henrion. Characterization of stability for cone increasing constraint mappings. Set-Valued Anal., 5(4):323–349, 1997.

88 [1559] Rene´ Henrion. A note on the connectedness of chance constraints. Stochastic Programming E-Print Series, http://www.speps.org, 2000. [1560] Rene´ Henrion. Qualitative stability of convex programs with probabilistic constraints. In Opti- mization (Namur, 1998), pages 164–180. Springer, Berlin, 2000. [1561] Rene´ Henrion. Structure and stability of probabilistic storage level constraints. Stochastic Pro- gramming E-Print Series, http://www.speps.org, 2000. [1562] Rene´ Henrion. Structure and stability of programs with probabilistic storage level constraints. In Stochastic optimization techniques (Neubiberg/Munich, 2000), volume 513 of Lecture Notes in Econom. and Math. Systems, pages 3–20. Springer, Berlin, 2002. [1563] Rene´ Henrion. Perturbation analysis of chance-constrained programs under variation of all constraint data. In Dynamic stochastic optimization (Laxenburg, 2002), volume 532 of Lecture Notes in Econom. and Math. Systems, pages 257–274. Springer, Berlin, 2004. [1564] Rene´ Henrion. Structural properties of linear probabilistic constraints. Stochastic Programming E-Print Series, http://www.speps.org, 2005. [1565] Rene´ Henrion. Some remarks on value-at-risk optimization. Stochastic Programming E-Print Series, http://www.speps.org, 2006. [1566] Rene´ Henrion, Christian Kuchler,¨ and Werner Romisch.¨ Scenario reduction in stochastic programming with respect to discrepancy distances. Stochastic Programming E-Print Series, http: //www.speps.org, 2006. [1567] Rene´ Henrion, Pu Li, Andris Moller,¨ Moritz Wendt, and Gunter¨ Wozny. Optimal control of a continuous distillation process under probabilistic constraints. In Online optimization of large scale systems, pages 499–517. Springer, Berlin, 2001. [1568] Rene´ Henrion, Li Pu, Andris Moller,¨ Marc C. Steinbach, Moritz Wendt, and Gunter¨ Wozny. Stochastic optimization for operating chemical processes under uncertainty. In Online optimization of large scale systems, pages 457–478. Springer, Berlin, 2001. [1569] Rene´ Henrion and Werner Romisch.¨ Metric regularity and quantitative stability in stochastic programs with probabilistic constraints. Math. Program., 84(1, Ser. A):55–88, 1999. [1570] Rene´ Henrion and Werner Romisch.¨ Stability of solutions to chance constrained stochastic programs. In Parametric optimization and related topics, V (Tokyo, 1997), pages 95–114. Lang, Frankfurt am Main, 2000. [1571] Rene´ Henrion and Werner Romisch.¨ Holder¨ and Lipschitz stability of solution sets in programs with probabilistic constraints. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [1572] Rene´ Henrion and Werner Romisch.¨ Lipschitz and differentiability properties of quasi-concave and singular normal distribution functions. Stochastic Programming E-Print Series, http://www. speps.org, 2005. [1573] Rene´ Henrion and Cyrille Strugarek. Convexity of chance constraints with independent random variables. Stochastic Programming E-Print Series, http://www.speps.org, 2006. [1574] Rene´ Henrion and Tamas Szantai. Properties and Calculation of Singular Normal Distributions. In S. Albers, R.H. Mohring,¨ G.Ch. Pﬂug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algo- rithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [1575] Antonio Heras and Ana G. Aguado. Stochastic goal programming. CEJOR Cent. Eur. J. Oper. Res., 7(3):139–158, 1999.

89 [1576] Ulrich Herkenrath and Radu Theodorescu. On a stochastic approximation procedure applied to the bandit problem. Elektron. Informationsverarb. Kybernet., 15(5-6):301–307, 1979. [1577] Ted Herman. Probabilistic self-stabilization. Inf. Process. Lett. 35, No.2, 63-67, 1990. [1578] Onesimo Hernandez-Lerma. Approximation and adaptive policies in discounted dynamic programming. Bol. Soc. Mat. Mex., II. Ser. 30, 25-35, 1985. [1579] Onesimo´ Hernandez-Lerma.´ Stochastic optimal control and infinite linear programming. In Sec- ond Symposium on Probability Theory and Stochastic Processes. First Mexican-Chilean Meeting on Stochastic Analysis (Spanish) (Guanajuato, 1992), volume 7 of Aportaciones Mat. Notas Inves- tigacion´ , pages 109–120. Soc. Mat. Mexicana, Mexico´ City, 1992. [1580] Morgan Herndon, Cary Perttunen, and Bruce Stuckman. Global optimization of a random walk function. Informatica, 3(2):198–224, 283, 291, 1992. [1581] Christian Hess. Convergence of conditional expectations for unbounded random sets, integrands, and integral functionals. Math. Oper. Res., 16(3):627–649, 1991. [1582] G.A. Heuer. On completely mixed strategies in bimatrix games. J. London math. Soc., II. Ser. 11, 17-20, 1975. [1583] Daniel P. Heyman and Matthew J. Sobel. Stochastic models in operations research., volume II: Stochastic optimization. of McGraw-Hill series in quantitative methods for management. New York etc.: McGraw-Hill book company., 1984. [1584] Norio Hibiki. Multi-period stochastic programming models using simulated paths for strategic asset allocation. J. Oper. Res. Soc. Japan, 44(2):169–193, 2001. [1585] J.L. Higle and S. Sen. Epigraphical nesting: a unifying theory for the convergence of algorithms. Journal of Optimization Theory and Applications 84:339-360, 1995. [1586] J.L. Higle and S. Sen. Stochastic decomposition: A statistical method for large scale stochastic linear programming. Kluwer Academic Publishers, Dordrecht, 1996. [1587] Julia L. Higle, James C. Bean, and Robert L. Smith. Deterministic equivalence in stochastic infinite horizon problems. Math. Oper. Res., 15(3):396–407, 1990. [1588] Julia L. Higle, Wing W. Lowe, and Ronald Odio. Conditional stochastic decomposition: An algorithmic interface for optimization and simulation. Oper. Res. 42, No.2, 311-322, 1994. [1589] Julia L. Higle and Suvrajeet Sen. Statistical verification of optimality conditions for stochastic programs with recourse. Ann. Oper. Res., 30(1-4):215–240, 1991. Stochastic programming, Part I (Ann Arbor, MI, 1989). [1590] Julia L. Higle and Suvrajeet Sen. Stochastic decomposition: an algorithm for two-stage linear programs with recourse. Math. Oper. Res., 16(3):650–669, 1991. [1591] Julia L. Higle and Suvrajeet Sen. On the convergence of algorithms with implications for stochastic and nondifferentiable optimization. Math. Oper. Res., 17(1):112–131, 1992. [1592] Julia L. Higle and Suvrajeet Sen. Finite master programs in regularized stochastic decomposition. Math. Programming, 67(2, Ser. A):143–168, 1994. [1593] Julia L. Higle and Suvrajeet Sen. Statistical approximations for recourse constrained stochastic programs. Ann. Oper. Res., 56:157–175, 1995. Stochastic programming (Udine, 1992). [1594] Julia L. Higle and Suvrajeet Sen. Duality and statistical tests of optimality for two stage stochastic programs. Math. Programming (Ser. B), 75(2):257–275, 1996. Approximation and computation in stochastic programming.

90 [1595] Julia L. Higle and Suvrajeet Sen. Stochastic decomposition, volume 8 of Nonconvex Optimization and its Applications. Kluwer Academic Publishers, Dordrecht, 1996. A statistical method for large scale stochastic linear programming. [1596] Julia L. Higle and Suvrajeet Sen. Statistical approximations for stochastic linear programming problems. Ann. Oper. Res., 85:173–192, 1999. Stochastic programming. State of the art, 1998 (Vancouver, BC). [1597] Julia L. Higle and Suvrajeet Sen. Algorithmic implications of duality in stochastic programs. In System modelling and optimization (Cambridge, 1999), pages 179–188. Kluwer Acad. Publ., Boston, MA, 2000. [1598] Julia L. Higle and Suvrajeet Sen. Multistage stochastic convex programs: duality and its implications. Ann. Oper. Res., 142:129–146, 2006. [1599] Julia L. Higle and Lei Zhao. Adaptive and nonadaptive samples in solving stochastic linear programs. Stochastic Programming E-Print Series, http://www.speps.org, 2005. [1600] Regina Hildenbrandt. Kostengunstige¨ Behandlung stochastischer Schwankungen der Bedarf- sgroßen¨ beim Transportproblem durch ein nichtlineares diskretes Optimierungsproblem. Opti- mization, 20(3):335–353, 1989. [1601] Raymond R. Hill and Charles H. Reilly. Multivariate composite distributions for coefficients in synthetic optimization problems. European J. Oper. Res., 121(1):64–77, 2000. [1602] S.D. Hill and M.C. Fu. Transfer optimization via simultaneous perturbation stochastic approximation. In C. Alexopoulos, K. Kang, W.R. Lilegdon, and D. Goldsman, editors, Proceedings of the Winter Simulation Conference, pages 242–249, 1995. [1603] Stacy D. Hill. Reduced gradient computation in prediction error identification. IEEE Trans. Autom. Control AC-30, 776-778, 1985. [1604] Randall S. Hiller and Jonathan Eckstein. Stochastic dedication: Designing fixed income portfolios using massively parallel Benders decomposition. Manage. Sci. 39, No.11, 1422-1438, 1993. [1605] Petri Hilli, Matti Koivu, Teemu Pennanen, and Antero Ranne. A stochastic programming model for asset liability management of a finnish pension company. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [1606] A.L. Hillman and P.L. Swan. Club participation under uncertainty. Econom. Lett., 4(4):307–312, 1979/80. [1607] K. Hinderer. Neuere Resultate in der stochastischen dynamischen Optimierung. Z. Angew. Math. Mech., 55(4):T16–T26, 1975. [1608] K. Hinderer and M. Stieglitz. A dynamic multi-item two-activity problem. OR Spektrum 15, No.2, 83-94, 1993. [1609] Karl Hinderer. Instationaere dynamische Optimierung bei schwachen Voraussetzungen ueber die Gewinnfunktionen. Abh. Math. Sem. Univ. Hamburg 36, 208-223, 1971. [1610] Karl Hinderer and Michael Stieglitz. Increasing and Lipschitz continuous minimizers in one- dimensional linear-convex systems without constraints: the continuous and the discrete case. Math. Methods Oper. Res., 44(2):189–204, 1996. [1611] K.F. Hinderer. On the structure of solutions of stochastic dynamic programs. In Proceedings of the seventh conference on probability theory (Bras¸ov, 1982), pages 173–182, Utrecht, 1985. VNU Sci. Press.

91 [1612] Ayman Hindy, Chi-fu Huang, and Steven H. Zhu. Numerical analysis of a free-boundary singular control problem in financial economics. J. Econom. Dynam. Control, 21(2-3):297–327, 1997. [1613] Ja. Hion. Ueber die Ganzzahligkeit der Ecken eines konvexen Polyeders. Ucenye Zapiski Tartu. gosudarst. Univ. 305, Trudy Mat. Meh. 12, 259-268, 1972. [1614] J. Hirche. Basishaufigkeit¨ bei linearen Restriktionen. Math. Operationsforsch. Statist. Ser. Optim., 10(1):27–37, 1979. [1615] J.-B. Hiriart-Urruty. Conditions necessaires´ d’optimalite´ pour un programme stochastique avec recours. SIAM J. Control Optimization, 16(2):317–329, 1978. [1616] J.-B. Hiriart-Urruty. Extension of Lipschitz integrands and minimization of nonconvex integral functionals. Applications to the optimal recourse problem in discrete time. Probab. Math. Statist., 3(1):19–36 (1983), 1982. [1617] J.B. Hiriart-Urruty. Algorithms of penalization type and of dual type for the solution of stochastic optimization problems with stochastic constraints. In Recent Dev. Stat., Proc. Eur. Meet. Stat. Grenoble 1976, 183-219, 1977. [1618] Jean-Baptiste Hiriart-Urruty. etude´ de quelques propriepergeometric integral. Trudy Sem. Kraev. Zadacamˇ , 10:90–94, 1973. [1619] Jean-Baptiste Hiriart-Urruty. Etude de quelques proprietes de la fonctionnelle moyenne et de l’inf- convolution continue en analyse convexe stochastique. C. r. Acad. Sci., Paris, Ser. A 280, 129-132, 1975. [1620] Jean-Baptiste Hiriart-Urruty. About properties of the mean value functional and of the continuous infimal convolution in stochastic convex analysis. In Optim. Tech., Part 2, Proc. 7th IFIP Conf., Nice 1975, Lect. Notes Comput. Sci 41, 763-789, 1976. [1621] Jean-Baptiste Hiriart-Urruty. Algorithmes stochastiques de type penalisation´ et de type dual pour les problemes` avec observations bruitees´ sur l’objectif et sur les contraintes. C.R. Acad. Sci. Paris Ser.´ A-B, 282(16):Aiii, A907–A910, 1976. [1622] Jean-Baptiste Hiriart-Urruty. Conditions necessaires´ d’optimalite´ pour un programme stochastique avec recours. C.R. Acad. Sci. Paris Ser. A-B, 283(13):Aii, A943–A946, 1976. [1623] Jean-Baptiste Hiriart-Urruty. Contributions a` la programmation mathematique:´ cas deterministe´ et stochastique. Universite´ de Clermont-Ferrand II, Clermont, 1977. These` present´ ee´ a` l’Universite´ de Clermont-Ferrand II pour obtenir le grade de Docteur es` Sciences Mathematiques,´ Serie´ E, No. 247. [1624] M. Hlynka and J.N. Sheahan. The secretary problem for a random walk. Stochastic Process. Appl., 28(2):317–325, 1988. [1625] Y.-C. Ho and D. L. Pepyne. Simple explanation of the no free lunch theorem of optimization. Kibernet. Sistem. Anal., (2):164–172, 191, 2002. [1626] Y.C. Ho and T.S. Chang. Another look at the nonclassical information structure problem. IEEE Trans. Autom. Control AC-25, 537-540, 1980. [1627] Yu-Chi Ho and Shu Li. Extensions of infinitesimal perturbation analysis. IEEE Trans. Autom. Control AC-33, No.5, 427-438, 1988. [1628] B. F. Hobbs and Y. D. Ji. Stochastic programming-based bounding of expected production costs for multiarea electric power systems. Operations Research, 47(6):836–848, 1999.

92 [1629] R. Hochreiter, G. Ch. Pflug, and D. Wozabal. Multi-stage stochastic electricity portfolio optimization in liberalized energy markets. In System modeling and optimization, volume 199 of IFIP Int. Fed. Inf. Process., pages 219–226. Springer, New York, 2006. [1630] Ronald Hochreiter. Scenario Optimization for Multi-Stage Stochastic Programming Problems. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algo- rithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [1631] A. Hoffman, J. Lee, and J. Williams. New upper bounds for maximum-entropy sampling. In mODa 6—advances in model-oriented design and analysis (Puchberg/Schneeberg, 2001), Contrib. Statist., pages 143–153. Physica, Heidelberg, 2001. [1632] Matthias Hoffmann. Verallgemeinerung eines stochastischen Quasigradientenverfahrens und seine Anwendung auf die Optimierung eines Bediensystems mit unbekannten parametern. Math. Oper- ationsforsch. Statist. Ser. Optim., 14(1):91–109, 1983. [1633] Balder von Hohenbalken and Gerhard Tintner. Mathematische Programmierung und ihre Anwen- dung auf die Wirtschaft. Z. Nationaloekonomie 34, 1-44, 1974. [1634] John H. Holland. Genetic algorithms and the optimal allocation of trials. SIAM J. Computing 2, 88-105, 1973. [1635] Kaj Holmberg. Efficient decomposition and linearization methods for the stochastic transportation problem. Comput. Optim. Appl., 4(4):293–316, 1995. [1636] Kaj Holmberg and Kurt O. Joernsten. Cross decomposition applied to the stochastic transportation problem. Eur. J. Oper. Res. 17, 361-368, 1984. [1637] K. Holmqvist, A. Migdalas, and P.M. Pardalos. Greedy randomized adaptive search for a location problem with economies of scale. In Developments in global optimization (Szeged, 1995), volume 18 of Nonconvex Optim. Appl., pages 301–313. Kluwer Acad. Publ., Dordrecht, 1997. [1638] Tito Homem-de-Mello. On the convergence of simulated annealing for discrete stochastic optimization. Stochastic Programming E-Print Series, http://www.speps.org, 2000. [1639] Tito Homem-de Mello. Estimation of derivatives of nonsmooth performance measures in regenerative systems. Math. Oper. Res., 26(4):741–768, 2001. [1640] Tito Homem-de Mello. Monte Carlo methods for discrete stochastic optimization. In Stochastic optimization: algorithms and applications (Gainesville, FL, 2000), pages 97–119. Kluwer Acad. Publ., Dordrecht, 2001. [1641] Tito Homem-de Mello. On rates of convergence for stochastic optimization problems under non- i.i.d. sampling. Stochastic Programming E-Print Series, http://www.speps.org, 2006. [1642] W. Honeit. Zum mathematischen Begriff des mehrstufigen Optimalsteuerungsproblems. Wiss. Z., Tech. Hochsch. Leipz. 6, 167-182, 1982. [1643] Han Hoogeveen and Marjan Van den Akker. Getting rid of stochasticity: applicable sometimes. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algo- rithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [1644] E. Hopfinger.¨ Dynamic programming of stochastic activity networks with cycles. In Optimization techniques (Proc. Ninth IFIP Conf., Warsaw, 1979), Part 2, volume 23 of Lecture Notes in Control and Information Sci., pages 309–315, Berlin, 1980. Springer. [1645] H.S. Hopkins. Experimental measurement of a 4-D phase space map of a heavy ion beam. Ph.D. thesis, Dept. of Nuclear Engineering, University of California, Berkeley, December 1997.

93 [1646] A. Hordijk and L.C.M. Kallenberg. Linear programming and Markov decision processes. In Oper. Res. Verf. 28, 2nd Symp. Oper. Res., Teil 1, Aachen 1977, 400-406 , 1978. [1647] Arie Hordijk. On the convergence of the average expected return in dynamic programming. J. math. Analysis Appl. 46, 542-544, 1974. [1648] V.Joseph Hotz and Robert A. Miller. Conditional choice probabilities and the estimation of dynamic models. Rev. Econ. Stud. 60, No.3, 497-529, 1993. [1649] J. V. Howard. Rendezvous search on the interval and the circle. Oper. Res., 47(4):550–558, 1999. [1650] H.R. Howson and N.G.F. Sancho. A new algorithm for the solution of multi-state dynamic programming problems. Math. Programming, 8:104–116, 1975. [1651] Kjetil Høyland, Michal Kaut, and Stein W. Wallace. A heuristic for moment-matching scenario generation. Computational Optimization and Applications, 24(2-3):169–185, 2003. [1652] Wei Shen Hsia. Bounds for the solution of a stochastic program with recourse. Bull. Inst. Math. Acad. Sinica, 4(2):307–311, 1976. [1653] Wei Shen Hsia. On a stochastic program with simple recourse. J. Math. Anal. Appl., 58(3):705– 712, 1977. [1654] Wei Shen Hsia. Probability density function of a stochastic linear programming problem. Naval Res. Logist. Quart., 24(3):417–424, 1977. [1655] Wei Shen Hsia. On a quadratic stochastic program with simple recourse. Bull. Inst. Math. Acad. Sinica, 7(1):87–97, 1979. [1656] Jin Yan Hu and Shao Lin Ji. A backward stochastic differential equation method for a stochastic optimization problem. Shandong Daxue Xuebao Ziran Kexue Ban, 36(3):282–286, 2001. [1657] C.C. Huang, I. Vertinsky, and W.T. Ziemba. Sharp bounds on the value of perfect information. Operations Res., 25(1):128–139, 1977. [1658] C.C. Huang, D.A. Wehrung, and W.T. Ziemba. A homogeneous distribution problem with applications to ﬁnance. Management Sci. 23, 297-304, 1976. [1659] C.C. Huang, W.T. Ziemba, and A. Ben-Tal. Bounds on the expectation of a convex function of a random variable: with applications to stochastic programming. Operations Res., 25(2):315–325, 1977. [1660] Haijun Huang, Shouyang Wang, and Michael G. H. Bell. A bi-level formulation and quasi-Newton algorithm for stochastic equilibrium network design problem with elastic demand. J. Syst. Sci. Complex., 14(1):40–53, 2001. [1661] Kai Huang and Shabbir Ahmed. The value of multi-stage stochastic programming in capacity planning under uncertainty. Stochastic Programming E-Print Series, http://www.speps.org, 2005. [1662] Nan-Jing Huang. A new class of random completely generalized strongly nonlinear quasi- complementarity problems for random fuzzy mappings. Korean J. Comput. Appl. Math., 5(2):315– 329, 1998. [1663] Siming Huang. Average number of iterations of some polynomial interior-point-algorithms for linear programming. Sci. China Ser. A, 43(8):829–835, 2000. [1664] G. Hubner.¨ Sequential similarity transformation for solving ﬁnite-stage sub-Markov decision problems. In Third Symposium on Operations Research (Univ. Mannheim, Mannheim, 1978), Section 3, volume 33 of Operations Res. Verfahren, pages 197–207. Hain, Konigstein/Ts.,¨ 1979.

94 [1665] Gerhard Hubner.¨ On the fixed points of the optimal reward operator in stochastic dynamic programming with discount factor greater than one. Z. Angew. Math. Mech., 57(8):477–480, 1977. [1666] J. Huelsmann. Spieltheoretische Ansaetze im stochastischen linearen Optimieren. In Oper. Res.- Verfahren 10, 236-243, 1970. [1667] J. Huelsmann. Optimale Entscheidungen im zweistufigen stochastischen Programmieren als Loe- sung linearer Programme. In Operations Res.-Verf. 14, 316-321, 1972. [1668] J. Hulsmann.¨ Zweistufiges stochastisches Programmieren bei Unsicherheit uber¨ die Verteilung von .A; b; c/. In Vierte Oberwolfach-Tagung uber¨ Operations Research (1971), Teil 2, pages 236–245. Operations Research–Verfahren, XIII, Meisenheim am Glan, 1972. Hain. [1669] Suwarna Hulsurkar, M.P. Biswal, and S.B. Sinha. Fuzzy programming approach to multi-objective stochastic linear programming problems. Fuzzy Sets and Systems, 88(2):173–181, 1997. [1670] David G. Humphrey and James R. Wilson. A revised simplex search procedure for stochastic simulation response surface optimization. INFORMS J. Comput., 12(4):272–283, 2000. [1671] Yong Liang Huo, San Yang Liu, and Li Yu. Hausdorff convergence of -approximate optimal solution sets in stochastic programming. Math. Appl. (Wuhan), 19(4):852–856, 2006. [1672] Mohammad Lotfy Hussein and Mohamed Abd El-Hady Kassem. Interactive stability of multiobjective nonlinear programming problems with stochastic parameters. J. Fuzzy Math., 4(3):503–512, 1996. [1673] Thong Nguyen Huu and Hao Tran Van. A stochastic algorithm for engineering optimization problems. Optimization Online, http://www.optimization-online.org, 2007. [1674] Chii-Ruey Hwang and Shuenn Jyi Sheu. Singular perturbed Markov chains and exact behaviors of simulated annealing processes. J. Theoret. Probab., 5(2):223–249, 1992. [1675] Masaaki Ida. Optimality on possibilistic linear programming with normal possibility distribution coefficient. Japanese J. Fuzzy Theory Systems, 7(3):349–360 (1996), 1995. [1676] M.G. Ierapetritou and E.N. Pistikopoulos. Global optimization for stochastic planning, scheduling and design problems. In Global optimization in engineering design, volume 9 of Nonconvex Optim. Appl., pages 231–287. Kluwer Acad. Publ., Dordrecht, 1996. [1677] G. Igelmund and F.J. Radermacher. Preselective strategies for the optimization of stochastic project networks under resource constraints. Networks, 13(1):1–28, 1983. [1678] Koji Iida, Ryusuke Hohzaki, and Takesi Kaiho. Optimal investigating search maximizing the detection probability. J. Oper. Res. Soc. Japan, 40(3):294–309, 1997. [1679] Tetsuo Iida. A non-stationary periodic review production-inventory model with uncertain production capacity and uncertain demand. European J. Oper. Res., 140(3):670–683, 2002. [1680] Dan V. Iliescu and Viorel Gh. Voda. Some notes on Pareto distribution. Rev. Roumaine Math. Pures Appl., 24(4):597–609, 1979. [1681] E.V. Iljin, A.V. Medvedev, and N.F. Novikov. On nonparametric algorithms of optimization. In Modelling and optimization of complex systems (Proc. IFIP-TC 7 Working Conf., Novosibirsk, 1978), volume 18 of Lecture Notes in Control and Information Sci., pages 198–206, Berlin, 1979. Springer. [1682] B. Illing. Spieltheoretische Problemstellungen in der stochastischen linearen Optimierung. In XV. Int. Wiss. Kolloquium Tech. Hochsch. Ilmenau 1970, Abt. A, 9-13 , 1970.

95 [1683] B. Illing. Zur Anwendung spieltheoretischer Methoden in der stochastischen linearen Optimierung. Wiss. Z. Tech. Hochsch. Ilmenau 16, No.2/3, 11-16, 1970. [1684] G. Infanger. Planning under Uncertainty: Solving Large-Scale Stochastic Linear Programs. Boyd and Fraser, Danvers, 1994. [1685] G. Infanger and D.P. Morton. Cut sharing for multistage stochastic linear programs with interstage dependency. Mathematical Programming, 75(2):241–256, 1996. [1686] Gerd Infanger. Monte Carlo (importance) sampling within a Benders decomposition algorithm for stochastic linear programs. Ann. Oper. Res., 39(1-4):69–95 (1993), 1992. [1687] Gerd Infanger. Stochastic programming for funding mortgage pools. Quant. Finance, 7(2):189– 216, 2007. [1688] R. Infante Mac´ias. Note on stochastic linear programming: evolution and present status. I. Trabajos Estadist.´ , 23(1-2):9–49, 1971. [1689] M. Inuiguchi. Stochastic programming problems versus fuzzy mathematical programming problems. Japanese J. Fuzzy Theory Systems, 4(1):97–109, 1992. [1690] Masahiro Inuiguchi and Masatoshi Sakawa. A possibilistic linear program is equivalent to a stochastic linear program in a special case. Fuzzy Sets and Systems, 76(3):309–317, 1995. [1691] A.D. Ioffe and D.B. Judin. Some non-linear problems o f stochastic programming. U.S.S.R. Com- put. Math. Math. Phys. 1 No.1, 207-225 (1972)., 1970. [1692] Hisao Ishibuchi and Hideo Tanaka. Interval 0-1 programming problem and product-mix analysis. J. Oper. Res. Soc. Japan 32, No.3, 352-370, 1989. [1693] H. Ishii and T. Matsutomi. Conﬁdence regional method of stochastic spanning tree problem. Math. Comput. Modelling, 22(10-12):77–82, 1995. Stochastic models in engineering, technology and management (Gold Coast, 1994). [1694] Hiroaki Ishii and Toshio Nishida. Stochastic linear knapsack problem. Tech. Rep. Osaka Univ., 32(1630-1651):25–30, 1982. [1695] Hiroaki Ishii and Toshio Nishida. Stochastic bottleneck spanning tree problem. Networks 13, 443-449, 1983. [1696] Hiroaki Ishii and Toshio Nishida. Stochastic linear knapsack problem: probability maximization model. Math. Japon., 29(2):273–281, 1984. [1697] Hiroaki Ishii and Toshio Nishida. The stochastic linear continuous type knapsack problem: a generalized P model. European J. Oper. Res., 19(1):118–124, 1985. [1698] Hiroaki Ishii, Toshio Nishida, and Yasunori Nanbu. A generalized chance constraint programming problem. J. Operations Res. Soc. Japan, 21(1):124–168, 1978. [1699] Hiroaki Ishii and Shogo¯ Shiode. Chance constrained bottleneck spanning tree problem. Ann. Oper. Res., 56:177–187, 1995. Stochastic programming (Udine, 1992). [1700] Hiroaki Ishii, Shogo¯ Shiode, and Toshio Nishida. Chance constrained spanning tree problem. J. Oper. Res. Soc. Japan, 24(2):147–158, 1981. [1701] Hiroaki Ishii, Shogo¯ Shiode, Toshio Nishida, and Yoshikazu Namasuya. Stochastic spanning tree problem. Discrete Appl. Math., 3(4):263–273, 1981. [1702] Hiroaki Ishii, Syogo Shiode, Toshio Nishida, and Katsurou Iguchi. An algorithm for a partially chance-constrained E-model. J. Oper. Res. Soc. Japan, 22(3):233–256, 1979.

96 [1703] Maged George Iskander. On solving stochastic fuzzy goal programming problem using a suggested interactive approach. J. Fuzzy Math., 9(2):437–446, 2001. [1704] Maged George Iskander. A fuzzy weighted additive approach for stochastic fuzzy goal programming. Appl. Math. Comput., 154(2):543–553, 2004. [1705] Maged George Iskander. Exponential membership function in stochastic fuzzy goal programming. Appl. Math. Comput., 173(2):782–791, 2006. [1706] Hiroyuki Itami. Expected objective value of a stochastic linear program and the degree of uncertainty of parameters. Management Sci., 21(3):291–301, 1974/75. [1707] M.N. Itbaev. Duality in problems of inexact and generalized linear programming. Izv. Akad. Nauk Kazakh. SSR Ser. Fiz.-Mat., 5:35–38, 1985. [1708] Alfredo N. Iusem. On dual convergence and the rate of primal convergence of Bregman’s convex programming method. SIAM J. Optim., 1(3):401–423, 1991. [1709] N.A. Ivanchuk. Analysis of the efﬁciency of some controlled search procedures. Problems Inform. Transmission, 19(1):25–33, 1983. [1710] Viktor Ivanovich Ivanenko. Information problems in control theory. Prace Nauk. Inst. Cybernet. Tech. Politech. Wroclaw. Ser. Konfer., 74(31):24–32, 1986. [1711] V.M. Ivanin. An estimate of the mathematical expectation of the number of elements of the Pareto set. Kibernetika (Kiev), 3:145–146, 1975. [1712] S.L. Ivanov. A method of search for a limit saddle point. Zh. Vychisl. Mat. i Mat. Fiz., 26(6):939– 941, 960, 1986. [1713] P.A. Ivashchenko. Adaptation in Economics. “Vishcha Shkola”, Kharkov, 1986. (in Russian). [1714] E.A. Ivushkina. Mathematical programming with randomness and fuzziness. In Fuzzy systems: modeling of structure and optimization (Russian), pages 76–82, Kalinin, 1987. Kalinin. Gos. Univ. [1715] Seiichi Iwamoto. Linear programming on recursive additive dynamic programming. J. Operations Res. Soc. Japan 18, 125-151, 1975. [1716] Seiichi Iwamoto. Conditional decision processes with recursive function. J. Math. Anal. Appl., 230(1):193–210, 1999. [1717] Seiichi Iwamoto. Recurrence formulas and decision tree tables in stochastic optimization. Surikaisekikenky¯ usho¯ Koky¯ uroku¯ , (1132):15–23, 2000. Mathematical decision theory under uncertainty and ambiguity (Japanese) (Kyoto, 1999). [1718] Seiichi Iwamoto. Fuzzy dynamic programming in the stochastic environment. In Dynamical aspects in fuzzy decision making, volume 73 of Stud. Fuzziness Soft Comput., pages 27–51. Physica, Heidelberg, 2001. [1719] Seiichi Iwamoto. Recursive method in stochastic optimization under compound criteria. In Ad- vances in mathematical economics, Vol. 3, pages 63–82. Springer, Tokyo, 2001. [1720] Kakuzo Iwamura and Baoding Liu. A genetic algorithm for chance constrained programming. J. Inform. Optim. Sci., 17(2):409–422, 1996. [1721] Yoh Iwasa. Pessimistic plant: Optimal growth schedule in stochastic environments. Theor. Popul. Biol. 40, No.2, 246-268, 1991. [1722] V.S. Izhutkin. Reduced gradient method for stochastic optimization problem with nonlinear constraints. Mosc. Univ. Comput. Math. Cybern. 1989, No.2, 102-104 translation from Vestn. Mosk. Univ., Ser. XV 1989, No.2, 79-81 (1989)., 1989.

97 [1723] Tommi Jaakkola, Michael I. Jordan, and Satinder P. Singh. On the convergence of stochastic iterative dynamic programming algorithms. Neural Comput. 6, No.6, 1185-1201, 1994. [1724] Jihad Jaam. Ramsey numbers by stochastic algorithms with new heuristics. In Combinatorics and computer science (Brest, 1995), volume 1120 of Lecture Notes in Comput. Sci., pages 163–181, Berlin, 1996. Springer. [1725] D. Jacobs, C.-T. Kuo, J.-T. Lim, and S.M. Meerkov. Improvability of serial production lines: theory and applications. In Recent advances in control and optimization of manufacturing systems, volume 214 of Lecture Notes in Control and Inform. Sci., pages 121–143. Springer, London, 1996. [1726] J. Jacobs, G. Freeman, J. Grygier, D. Morton, G. Schultz, K. Staschus, and J. Stedinger. Socrates: A system for scheduling hydroelectric generation under uncertainty. Annals of Operations Research, 59:99–133, 1995. [1727] O.L.R. Jacobs, M.H.A. Davis, M.A.H. Dempster, C.J. Harris, and P.C. Parks, editors. Analysis and Optimization of Stochastic Systems. Academic Press, London, 1980. [1728] Sheldon H. Jacobson and Lee W. Schruben. Techniques for simulation response optimization. Oper. Res. Lett., 8(1):1–9, 1989. [1729] R. Jagannathan. Chance-constrained programming with joint constraints. Operations Res., 22(2):358–372, 1974. [1730] R. Jagannathan. Minimax procedure for a class of linear programs under uncertainty. Operations Res., 25(1):173–177, 1977. [1731] R. Jagannathan. A minimax procedure for a class of stochastic programs. In Quantitative planning and control, Essays in Honor of W. W. Cooper, 23-35 , 1979. [1732] R. Jagannathan. Use of sample information in stochastic recourse and chance-constrained programming models. Management Sci., 31(1):96–108, 1985. [1733] R. Jagannathan. A stochastic geometric programming problem with multiplicative recourse. Oper. Res. Lett., 9(2):99–104, 1990. [1734] R. Jagannathan and M.R. Rao. A class of nonlinear chance-constrained programming models with joint constraints. Operations Res. 21, 360-364, 1973. [1735] Raj Jagannathan. Linear programming with stochastic processes as parameters as applied to production planning. Ann. Oper. Res., 30(1-4):107–114, 1991. Stochastic programming, Part I (Ann Arbor, MI, 1989). [1736] Patrick Jaillet. Stochastic routing problems. In Stochastics in combinatorial optimization, Adv. Sch. CISM, Udine/Italy 1986, 197-213, 1987. [1737] Patrick Jaillet. Analysis of probabilistic combinatorial optimization problems in Euclidean spaces. Math. Oper. Res., 18(1):51–70, 1993. [1738] Patrick Jaillet and Amedeo R. Odoni. The probabilistic vehicle routing problem. In Vehicle routing: Methods and studies, Stud. Manage. Sci. Syst. 16, 293-318 , 1988. [1739] Anjani Jain and John W. Mamer. Approximations for the random minimal spanning tree with application to network provisioning. Oper. Res. 36, No.4, 575-584, 1988. [1740] Andrzej Jakubowski. Stochastic model of resource allocation to R & D activities under cost value uncertainty. In Optim. Techn., Proc. IFIP Conf., Wuerzburg 1977, Part 2, Lect. Notes Control Inf. Sci. 7, 411-421, 1978.

98 [1741] Udom Janjarassuk and Jeff Linderoth. Reformulation and sampling to solve a stochastic network interdiction problem. Optimization Online, http://www.optimization-online.org, 2006. [1742] O. Janssens de Bisthoven, P. Schuchewytsch, and Y. Smeers. Power generation planning with uncertain demand. In Numerical techniques for stochastic optimization, Springer Ser. Comput. Math. 10, 465-480, 1988. [1743] C. Jansson and S.M. Rump. Rigorous solution of linear programming problems with uncertain data. Z. Oper. Res. 35, No.2, 87-111, 1991. [1744] Elzbieta Jasinska and Leszek Jerzy Jasinski. The network models of multi-activity projects as stochastic programming problems. Przegl. Stat. 28, 215-223, 1981. [1745] Leszek Jerzy Jasinski.´ Game theory method in stochastic programming. Przeglk ad Statyst., 23(1):107–117, 1976. [1746] Leszek Jerzy Jasinski.´ A priori information in stochastic programming. Przeglk ad Statyst., 26(1- 2):35–47 (1980), 1979. [1747] Leszek Jerzy Jasinski. The linear stochastic distribution problem. The Charnes-Cooper approach. Przegl. Stat. 37, No.4, 327-338, 1990. [1748] Leszek Jerzy Jasinski. Stochastic distribution problem. The Dantzig-Madansky approach. Przegl. Stat. 38, No.1, 71-83, 1991. [1749] Leszek Jerzy Jasinski´ and Andrzej Tabeau. Stochastic programming problems with a known probability of fulﬁlling a set of constraints. Przeglk ad Statyst., 28(1-2):107–116 (1982), 1981. [1750] A.I. Jastremskii. Ueber das einfachste stochastische Interbranchenmodell der Optimierung. Kiber- netika, Kiev 1973, Nr. 5, 139-140, 1973. [1751] A.I. Jastremskii. Duality in two-phase stochastic programming and a stochastic linear production model. Kibernetika (Kiev), 2:141–145, 1975. [1752] A.I. Jastremskii. Wachstumstempi und Effektivitaetsnorm im optimalen Plan eines dynamischen stochastischen Produktionsmodells. Kibernetika, Kiev 1976, Nr. 3, 110-114, 1976. [1753] A.I. Jastremskii and E.` Vol’kenstain.ˇ Randomness of demand and stochastic models of industrial production. Issled. Operatsii i ASU, 13:112–116, 136, 1979. [1754] A.V. Jazenin. Man-machine procedures in decision-making problems with fuzzy goals. In Math- ematical methods of optimization and structuring of systems (Russian), pages 88–92, 184. Kalin- ingrad. Gos. Univ., Kaliningrad, 1979. [1755] A.V. Jazenin and G.P. Diskant.ˇ A linear decision-making problem with fuzzy goals. In Mathemat- ical methods of optimization and structuring of systems (Russian), pages 77–87, 183. Kaliningrad. Gos. Univ., Kaliningrad, 1979. [1756] T.R. Jefferson and C.H. Scott. Geometric programming with probabilistic decision variables. J. Austral. Math. Soc. Ser. B, 22(2):229–236, 1980/81. [1757] Larry Jenkins and Murray Anderson. A multivariate statistical approach to reducing the number of variables in data envelopment analysis. European J. Oper. Res., 147(1):51–61, 2003. [1758] Peter Jennergren. A note on a Dantzig-Wolfe decomposition-like method for solving a particular resource-allocation problem under uncertainty. Math. Operationsforsch. Statistik 4, 127-132, 1973. [1759] Max E. Jerrell and Wendy A. Campione. Global optimization of econometric functions. J. Global Optim., 20(3-4):273–295, 2001. Special issue: Applications to economics.

99 [1760] Elizabeth R. Jessup, Dafeng Yang, and Stavros A. Zenios. Parallel factorization of structured matrices arising in stochastic programming. SIAM J. Optim., 4(4):833–846, 1994. [1761] Jully Jeunet and Nicolas Jonard. Single-point stochastic search algorithms for the multi-level lot- sizing problem. Comput. Oper. Res., 32(4):985–1006, 2005. [1762] Nand K. Jha. Stochastic mathematical modelling and manufacturing cost estimation in uncertain industrial environment. Int. J. Prod. Res. 30, No.12, 2755-2771, 1992. [1763] X.D. Ji and B.D. Familoni. A diagonal recurrent neural network-based hybrid direct adaptive SPSA control system. IEEE Transactions on Automatic Control, 44:1469–1473, 1999. [1764] Xiaoyu Ji. Models and algorithm for stochastic shortest path problem. Appl. Math. Comput., 170(1):503–514, 2005. [1765] H. Jiang and L. Qi. Globally and superlinearly convergent trust-region algorithm for convex sc1-minimization problems and its application to stochastic programs. J. Optim. Theory Appl., 90(3):649–669, 1996. [1766] Henrik Joensson, Kurt Joernsten, and Edward A. Silver. Application of the scenario aggregation approach to a two-stage, stochastic, common component, inventory problem with a budget constraint. Eur. J. Oper. Res. 68, No.2, 196-211, 1993. [1767] Tor A. Johansen, Rene´ van de Molengraft, and Henk Nijmeijer, editors. Switched, piecewise and polytopic linear systems. Taylor & Francis Ltd., Abingdon, 2002. Internat. J. Control 75 (2002), no. 16-17. [1768] Andrew E.W. Jones and G.W. Forbes. An adaptive simulated annealing algorithm for global optimization over continuous variables. J. Global Optim., 6(1):1–37, 1995. [1769] Stephen K. Jones, Ralph K. Cavin III, and William M. Reed. Analysis of error-gradient adaptive linear estimators for a class of stationary dependent processes. IEEE Trans. Inf. Theory IT-28, 318-329, 1982. [1770] T. W. Jonsbraten.˚ Oil ﬁeld optimization under price uncertainty. Journal of the Operational Re- search Society, 49(8):811–818, 1998. [1771] Tore W. Jonsbraten,˚ Roger J.-B. Wets, and David L. Woodruff. *a class of stochastic programs with decision dependent random elements. Ann. Oper. Res., 82:83–106, 1998. Modelling: in memory of Asa˚ Hallefjord. [1772] J.S. Jordan. Information and shadow prices for the constrained concave team problem. J. math. Economics 2, 371-393, 1975. [1773] Tibor Jordan and Alessandro Panconesi, editors. Probabilistic methods in combinatorial optimization. John Wiley & Sons Inc., New York, 2002. Random Structures Algorithms 20 (2002), no. 3. [1774] S. Jorjani, C.H. Scott, and D.L. Woodruff. Selection of an optimal subset of sizes. International Journal of Production Research, 37:3697–3710, 1999. [1775] Rajani R. Joshi. A new heuristic algorithm for probabilistic optimization. Comput. Oper. Res., 24(7):687–697, 1997. [1776] R.R. Joshi and D.K. Satyanarayana. A nested layered network model for parallel solutions of discrete SPPs. Comput. Math. Appl., 33(5):111–123, 1997. [1777] Sumit Joshi. Recursive utility, martingales, and the asymptotic behaviour of optimal processes. J. Econom. Dynam. Control, 21(2-3):505–523, 1997.

100 [1778] S.F. Jozwiak. Probability-based optimization of truss structures. Comput. Struct. 32, No.1, 87-91, 1989. [1779] Stanislaw F. Jozwiak. Minimum weight design of structures with random parameters. Comput. Struct. 23, 481-485, 1986. [1780] E.` Jubi. Finding the optimal randomized solution in M- and P-models of stochastic programming. Eesti NSV Tead. Akad. Toimetised Fu¨us.-Mat.¨ , 26(1):64–71, 1977. [1781] E.` Jubi. A statistical study and method for the solution of stochastic programming problems. Eesti NSV Tead. Akad. Toimetised Fu¨us.-Mat.¨ , 26(4):369–375, 1977. [1782] James V. Jucker and Robert C. Carlson. The simple plant-location problem under uncertainty. Operations Res. 2 1045-1055 (1977)., 1976. [1783] Joaquim J. Judice,´ Hanif D. Sherali, and Isabel M. Ribeiro. The eigenvalue complementarity problem. Comput. Optim. Appl., 37(2):139–156, 2007. [1784] A.D. Judin. Dualitaet in der mehretappenweisen stochastischen Programmierung. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1973, Nr. 6, 24-31, 1973. [1785] A.D. Judin. Koordinatenweiser Abstieg in Problemen der unendlichdimensionalen konvexen Pro- grammierung. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1974, Nr. 1, 34-42, 1974. [1786] D.B. Judin. Methods of constructing decision rules for multistage problems of stochastic programming. Sov. Math., Dokl. 14, 824-828 translation from Dokl. Akad. Nauk SSSR 210, 779-782 (1973)., 1973. [1787] D.B. Judin. Multistage problems of stochastic programming. Sov. Math., Dokl. 14, 787-790 translation from Dokl. Akad. Nauk SSSR 210, 545-548 (1973)., 1973. [1788] D.B. Judin. Mathematische Methoden der Steuerung bei unvollstaendiger Information. Aufgaben und Methoden der stochastischen Programmierung. (Matematiceskie metody upravlenija v uslovi- jah nepolnoi informacii. Zadaci i metody stohasticeskogo programmirovanija.). Moskau: ’Sovet- skoe Radio’, 1974. [1789] D.B. Judin and T.D. Beresnewa. Statische und dynamische Modelle der stochastischen Opti- mierung. In Math.-oekon. Meth. Modelle, 105-152, 1977. [1790] D.B. Judin and E.` V. Coi. A priori decision rules in multistage stochastic programming problems. Ekonom.` i Mat. Metody, 9:947–961, 1973. [1791] D.B. Judin and E.´ V. Coi. A qualitative study of certain classes of stochastic problems. Kibernetika (Kiev), 2:73–77, 1975. [1792] D.B. Judin and E.V. Coi. Ganzzahlige stochastische Programmierung. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1974, Nr. 1, 3-11, 1974. [1793] D.B. Judin and E.V. Coi. Qualitative Untersuchung einiger Klassen stochastischer Probleme. Kibernetika, Kiev 1975, Nr. 2, 73-77, 1975. [1794] Ghassan Kabbara. New utilization of fuzzy optimization method. In Fuzzy information and decision processes, 239-246, 1982. [1795] D.G. Kabe. On some coverage probability maximization problems. Commun. Stat., Simulation Comput. B9, 73-79, 1980. [1796] Janusz Kacprzyk and Piotr Staniewski. A new approach to the control of stochastic systems in a fuzzy environment. Arch. Automat. Telemech., 25(4):433–444 (1981), 1980.

101 [1797] D.P. Kakabadze, G.M. Kubintsev, and V.A. Taran. Control of the random step distribution function in a discrete adaptive system. Automat. Remote Control, 41(2):217–224, 1980. [1798] V.A. Kaladze and Ya.S. Rubinshtejn. Convergence of the random search method in the neighbor- hood of the extremum. Avtomat. vycislit. Tehn., Riga 1972, No.3, 67, 1972. [1799] V.A. Kaladze and Ya.S. Rubinshtejn. Polar modification of random search. Avtomat. vycislit. Tehn., Riga 1972, No.2, 58, 1972. [1800] Osmo Kaleva. A note on fixed points for fuzzy mappings. Fuzzy Sets and Systems, 15(1):99–100, 1985. [1801] E.` V. Kalinina, Ja. I. Hurgin, and A.G. Sapiro.ˇ Stable distributions in problems of stochastic programming. In Mathematical methods of solution of economic problems, No. 8 (Russian), pages 134–138, Moscow, 1979. “Nauka”. [1802] P. Kall. Some remarks on the distribution problem of stochastic linear programming. In Operations Res.-Verf. 16, 189-196, 1973. [1803] P. Kall. Stochastische Optimierung—einige neuere Ergebnisse. In Fortschritte in der mathematischen Optimierung (Tagung, Humboldt Univ., Berlin, 1978), volume 15 of Seminarberichte, pages 52–64. Humboldt Univ. Berlin, 1978. [1804] P. Kall. Solving complete fixed recourse problems by successive discretization. In Recent results in stochastic programming, Proc., Oberwolfach 1979, Lect. Notes Econ. Math. Syst. 179, 135-138, 1980. [1805] P. Kall. Stochastic programming. European J. Oper. Res., 10(2):125–130, 1982. [1806] P. Kall. Stochastic programs with recourse: an upper bound and the related moment problem. Z. Oper. Res. Ser. A-B, 31(3):A119–A141, 1987. [1807] P. Kall. Stochastic programming with recourse: upper bounds and moment problems—a review. In Advances in mathematical optimization, volume 45 of Math. Res., pages 86–103, Berlin, 1988. Akademie-Verlag. [1808] P. Kall. An upper bound for SLP using first and total second moments. Ann. Oper. Res., 30(1- 4):267–276, 1991. Stochastic programming, Part I (Ann Arbor, MI, 1989). [1809] P. Kall. A survey of approximation methods in stochastic programming. In Optimization: models, methods, solutions (Russian) (Irkutsk, 1989), pages 125–133. “Nauka” Sibirsk. Otdel., Novosi- birsk, 1992. [1810] P. Kall. Solution methods in stochastic programming. In System modelling and optimization (Compiegne,` 1993), volume 197 of Lecture Notes in Control and Inform. Sci., pages 3–22. Springer, London, 1994. [1811] P. Kall. Bounds for and approximations to stochastic linear programs with recourse—tutorial. In Stochastic programming methods and technical applications (Neubiberg/Munich, 1996), pages 1–21. Springer, Berlin, 1998. [1812] P. Kall and J. Mayer. A model management system for stochastic linear programming. In System modelling and optimization (Zurich, 1991), volume 180 of Lecture Notes in Control and Inform. Sci., pages 580–587. Springer, Berlin, 1992. [1813] P. Kall and J. Mayer. SLP-IOR: A model management system for stochastic linear programming - system design. In A.J.M. Beulens and H.-J. Sebastian, editors, Optimization-Based Computer- Aided Modelling and Design, pages 139–157. Springer-Verlag, Berlin etc., 1992.

102 [1814] P. Kall and J. Mayer. SLP-IOR: on the design of a workbench for testing SLP codes. Investigacion´ Oper., 14(2-3):148–161, 1993. Workshop on Stochastic Optimization: the State of the Art (Havana, 1992). [1815] P. Kall and J. Mayer. Computer support for modeling in stochastic linear programming. In Stochas- tic programming (Neubiberg/Munchen,¨ 1993), volume 423 of Lecture Notes in Econom. and Math. Systems, pages 54–70. Springer, Berlin, 1995. [1816] P. Kall and J. Mayer. On testing SLP codes with SLP-IOR. Manuscript, Inst. Oper. Res., University of Zurich, 1996. Accepted for Proceedings Matrah´ aza´ 1996. [1817] P. Kall and J. Mayer. On solving stochastic linear programming problems. In Stochastic programming methods and technical applications (Neubiberg/Munich, 1996), pages 329–344. Springer, Berlin, 1998. [1818] P. Kall and J. Mayer. On the role of bounds in stochastic linear programming. Optimization, 47(3- 4):287–301, 2000. Numerical methods for stochastic optimization and real-time control of robots (Neubiberg/Munich, 1998). [1819] P. Kall and W. Oettli. Measurability theorems for stochastic extremals. SIAM J. Control, 13(5):994– 998, 1975. [1820] P. Kall and W. Oettli. Measurability theorems for stochastic extremals (extended abstract). In Siebente Oberwolfach-Tagung uber¨ Operations Research (1974), Operations Research Verfahren, Band XXI, pages 139–140, Meisenheim am Glan, 1975. Hain. [1821] P. Kall and Werner Oettli. Measurability theorems for stochastic extremals. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 93–95, London, 1980. Academic Press. [1822] P. Kall, A. Ruszczynski,´ and K. Frauendorfer. Approximation techniques in stochastic programming. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 33–64. Springer, Berlin, 1988. [1823] P. Kall and D. Stoyan. Solving stochastic programming problems with recourse including error bounds. Math. Operationsforsch. Statist. Ser. Optim., 13(3):431–447, 1982. [1824] P. Kall and S.W. Wallace. Stochastic Programming. Wiley, Chichester etc., 1994. [1825] Peter Kall. Approximations to stochastic programs with complete ﬁxed recourse. Numer. Math., 22:333–339, 1974. [1826] Peter Kall. Stochastic linear programming. Springer-Verlag, Berlin, 1976. Okonometrie¨ und Unternehmensforschung, No. XXI. [1827] Peter Kall. Computational methods for solving two-stage stochastic linear programming problems. Z. Angew. Math. Phys., 30(2):261–271, 1979. [1828] Peter Kall. Towards computing the expected value of perfect information. In Mathematische Systeme in der Oekonomie, R. Henn z. 60. Geb., 277-287 , 1983. [1829] Peter Kall. On approximations and stability in stochastic programming. In Parametric optimization and related topics (Plaue, 1985), volume 35 of Math. Res., pages 387–407, Berlin, 1987. Akademie-Verlag. [1830] Peter Kall and Janos´ Mayer. SLP-IOR: an interactive model management system for stochastic linear programs. Math. Programming, 75(2, Ser. B):221–240, 1996. Approximation and computation in stochastic programming.

103 [1831] Peter Kall and Janos´ Mayer. Modeling support for multistage recourse problems. In Dynamic stochastic optimization (Laxenburg, 2002), volume 532 of Lecture Notes in Econom. and Math. Systems, pages 21–41. Springer, Berlin, 2004. [1832] Peter Kall and Janos´ Mayer. Building and solving stochastic linear programming models with SLP-IOR. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 79–93. SIAM, Philadelphia, PA, 2005. [1833] Peter Kall and Janos Mayer. Stochastic Linear Programming: Models, Theory, and Computation, volume 80 of International Series in Operations Research & Management Science. Springer, 2005. [1834] Peter Kall and Janos´ Mayer. Some insights into the solution algorithms for SLP problems. Ann. Oper. Res., 142:147–164, 2006. [1835] Peter Kall and Andras´ Prekopa,´ editors. Recent results in stochastic programming, volume 179 of Lecture Notes in Economics and Mathematical Systems, Berlin, 1980. Springer-Verlag. [1836] J.G. Kallberg, R.W. White, and W.T. Ziemba. Short term financial planning under uncertainty. Manage. Sci. 28, 670-682, 1982. [1837] J.G. Kallberg and W.T. Ziemba. An extended Frank-Wolfe algorithm with application to portfolio selection problems. In Recent results in stochastic programming, Proc., Oberwolfach 1979, Lect. Notes Econ. Math. Syst. 179, 139-162, 1980. [1838] J.G. Kallberg and W.T. Ziemba. Generalized concave functions in stochastic programming and portfolio theory. In Generalized concavity in optimization and economics, Proc. NATO Adv. Study Inst., Vancouver/Can. 1980, 719-767, 1981. [1839] L. Kallenberg. Special solution methods for replacement problems. In Operations Research Pro- ceedings, 2000 (Dresden), pages 87–90, Berlin, 2001. Springer. [1840] L.C.M. Kallenberg. Z. Oper. Res., (1). [1841] L.C.M. Kallenberg. Linear programming to compute a bias-optimal policy. In Operations research proceedings 1981 (Gottingen)¨ , pages 433–440. Springer, Berlin, 1982. [1842] L.C.M. Kallenberg. Survey of linear programming for standard and nonstandard Markovian control problems. II. Applications. Z. Oper. Res., 40(2):127–143, 1994. [1843] Markku Kallio and William T. Ziemba. Arbitrage pricing simplified. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [1844] Sofia Kalpazidou. Optimal transforms by two predictable processes. Bull. Math. Soc. Sci. Math. Repub. Soc. Roum., Nouv. Ser. 30(78), 313-319, 1986. [1845] Basil A. Kalymon. An optimization algorithm for a linear model of a simulation system. Manage- ment Sci., Theory 21, 516-530, 1975. [1846] M.M. Kamilov and Sh. Kh. Fazylov. Optimization in pattern recognition problems. In Random search and pattern recognition (Russian), pages 11–17, 118. “Fan”, Tashkent, 1985. [1847] V.A. Kaminskas and V.A. Pukas. On a numerical method for solving a two-stage nonlinear stochastic problem. In Issled. Algoritm. Ocen. Paramet. din. Sist. Process., Mater. Semin. Inst. Fiz. Mat. AN Litov. SSR, Stat. Probl. Upr. 16, 120-127, 1976. [1848] V.A. Kaminskii. Correlation constraints in stochastic optimization problems. Kibernetika (Kiev), 4:122–124, 136, 1986. [1849] V.N. Kaminskij. Optimization of closed stochastic networks with exponential servicing. Eng. Cybern. 18, No.6, 57-64 translation from Izv. Akad. Nauk SSSR, Tekh. Kibern. 1980, No.6, 68-76 (1980)., 1980.

104 [1850] T. Kampke.¨ Tight bounds for capacities. Comput. Math. Appl., 27(8):67–86, 1994. [1851] Yu. S. Kan. Optimization of control by the quantile criterion. Avtomat. i Telemekh., (5):77–88, 2001. [1852] Yu. S. Kan and A. I. Kibzun. Sensitivity analysis of worst-case distribution for probability optimization problems. In Probabilistic constrained optimization, volume 49 of Nonconvex Optim. Appl., pages 132–147. Kluwer Acad. Publ., Dordrecht, 2000. [1853] Yu. S. Kan and A.I. Kibzun. Convexity properties of probability and quantile functions in optimization problems. Avtomat. i Telemekh., 3:82–102, 1996. [1854] Yu. S. Kan and A. A. Mistryukov. On the equivalence in stochastic programming with probability and quantile objectives. In Stochastic programming methods and technical applications (Neu- biberg/Munich, 1996), pages 145–153. Springer, Berlin, 1998. [1855] Yu. S. Kan and A. V. Rusyaev. The quantile minimization problem with a bilinear loss function. Avtomat. i Telemekh., 7:67–75, 1998. [1856] Yu. S. Kan and N. V. Tuzov. Quantile minimization of the normal distribution of a bilinear loss function. [1857] Yuri Kan. Application of the quantile optimization to bond portfolio selection. In Stochastic optimization techniques (Neubiberg/Munich, 2000), volume 513 of Lecture Notes in Econom. and Math. Systems, pages 285–308. Springer, Berlin, 2002. [1858] O. N. Kaneva. A two-stage nonlinear stochastic programming problem with a deterministic com- pensation matrix. In Mathematical structures and modeling. No. 14 (Russian), pages 25–33. Omsk. Gos. Univ., Omsk, 2004. [1859] I. Ju. Kaniovskaja. Convergence of random processes generated by a procedure of the stochastic approximation type. In Methods of solution of problems of nonsmooth optimization and stochastic programming (Russian), pages 18–25, 35. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1979. [1860] I. Yu. Kaniovskaya. Asymptotic properties of Fabian’s algorithm with nonsmooth regression functions. Issled. Operatsii i ASU, 23:29–35, 139, 1984. [1861] Yu.M. Kaniovski, P.S. Knopov, and Z.V. Nekrylova. Limit Theorems for Stochastic Programming Processes. Naukova dumka, Kiev, 1980. (in Russian). [1862] Yuri M. Kaniovski, Alan J. King, and Roger J.-B. Wets. Probabilistic bounds (via large deviations) for the solutions of stochastic programming problems. Ann. Oper. Res., 56:189–208, 1995. Stochastic programming (Udine, 1992). [1863] Ju. M. Kaniovskii. The asymptotic normality of a stochastic minimization method. In Methods of operations research and of reliability theory in systems analysis (Russian), pages 63–69, Kiev, 1977. Akad. Nauk. Ukrain. SSR Inst. Kibernet. [1864] Ju. M. Kaniovskii. A way of controlling the calculation accuracy in the statistical gradient method. Kibernetika (Kiev), 5:87–89, 1978. [1865] Ju. M. Kaniovskii. Asymptotic properties of a stochastic method of minimization. In Operations research (models, systems, solutions), No. 7 (Russian), pages 24–36, 1, Moscow, 1979. Akad. Nauk SSSR Vychisl. Tsentr. [1866] Ju. M. Kaniovskii, P.S. Knopov, and Z.V. Nekrylova. The stochastic programming method in Hilbert space. Kibernetika (Kiev), 6:71–79, 1978. [1867] Ju. M. Kaniovskii, P.S. Knopov, and Z.V. Nekrylova. Predel’ nye teoremy dlya protsessov stokhasticheskogo programmirovaniya. “Naukova Dumka”, Kiev, 1980.

105 [1868] Yu. M. Kaniovskii. Estimating the error in direct methods of stochastic programming. Cybernetics, 16(5):768–775 (1981), 1980. [1869] Yu. M. Kaniovskii. Estimation of errors in construction of conﬁdence intervals in some stochastic programming methods. Cybernetics, 17(1):121–125, 1981. [1870] Yu. M. Kaniovskii. A limit theorem for processes of stochastic optimization and estimation with constant step. Dokl. Akad. Nauk SSSR, 261(1):18–20, 1981. [1871] Yu. M. Kaniovskii. Asymptotic properties of a stochastic analogue of the gradient method of optimization in a Hilbert space. Issled. Operatsii i ASU, 20:55–69, 1982. [1872] Yu. M. Kaniovskii. Comparison of the rates of convergence of two-step and one-step methods of stochastic programming. Dokl. Akad. Nauk Ukrain. SSR Ser. A, 7:70–73, 1982. [1873] Yu. M. Kaniovskii. A stochastic analogue of the conjugate gradient method with a ﬁxed step. Issled. Operatsii i ASU, 21:3–8, 1983. [1874] Yu. M. Kaniovskii. Fabian’s algorithm in the theory of self-adjusting systems. Avtomat. i Telemekh., 11:66–69, 1984. [1875] Yu. M. Kaniovskii. Stochastic optimization algorithms with slowly decreasing step multiplier. Kibernetika (Kiev), 4:iii, 102–106, 135, 1984. [1876] Yu. M. Kaniovskii and P.S. Knopov. Asymptotic properties of some stochastic approximation methods. Cybernetics, 15(5):727–734 (1980), 1979. [1877] Yu. M. Kaniovskii and G.G. Murauskas. Asymptotic properties of the stochastic method of La- grange multipliers. In Theory of optimal decisions, pages 78–84, 114, Kiev, 1982. Akad. Nauk Ukrain. SSR Inst. Kibernet. [1878] Yu.M. Kaniovskij. Limit theorems for random processes, and stochastic Markov recurrent procedures. Cybernetics 15, 917-927 translation from Kibernetika 1979, No.6, 127-130 (1979)., 1980. [1879] Yu.M. Kaniovskij. On a certain method of random search. Zh. Vychisl. Mat. Mat. Fiz. 21, 499-503, 1981. [1880] Yu.M. Kaniovskij. Comparison of the convergence rates of the two-step and one-step methods of stochastic programming. Dokl. Akad. Nauk Ukr. SSR, Ser. A 1982, No.7, 70-73, 1982. [1881] Yu.M. Kaniovskij. Stochastical analogue of the method of conjugated gradients with constant increment. Issled. Oper. ASU 21, 3-8, 1983. [1882] Yu.M. Kaniovskij. The limit theorem for optimization and estimation algorithms with a variable step. Dokl. Akad. Nauk Ukr. SSR, Ser. A 1985, No.1, 59-61, 1985. [1883] Yu.M. Kaniovskij, P.S. Knopov, and Z.V. Nekrylova. Stochastic programming in Hilbert space. Cybernetics 14, 878-888 translation from Kibernetika, No.6, 71-79 (1978)., 1979. [1884] Yu.M. Kaniovskij, P.S. Knopov, and Z.V. Nekrylova. Limit theorems for processes of stochastic programming. (Predel’nye teoremy dlya protsessov stokhasticheskogo programmirovaniya). Akademiya Nauk Ukrainskoj SSR, Ordena Lenina Institut Kibernetiki. Kiev: ”Naukova Dumka”., 1980. [1885] V. Kankovˇ a.´ Estimates in stochastic programming—chance constrained case. Problems Control Inform. Theory/Problemy Upravlen. Teor. Inform., 18(4):251–260, 1989. [1886] V. Kankovˇ a.´ A note on multistage stochastic programming with individual probability constraints. In Operations Research Proceedings, 2000 (Dresden), pages 91–96, Berlin, 2001. Springer.

106 [1887] V. Kankovˇ a.´ A remark on the analysis of multistage stochastic programs: Markov dependence. ZAMM Z. Angew. Math. Mech., 82(11-12):781–793, 2002. 4th GAMM-Workshop “Stochastic Models and Control Theory” (Lutherstadt Wittenberg, 2001). [1888] Vlasta Kankovˇ a.´ An approximative solution of a stochastic optimization problem. In Transactions of the Eighth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Prague, 1978), Vol. A, pages 349–353. Reidel, Dordrecht, 1978. [1889] Vlasta Kankovˇ a.´ Differentiability of the optimal function in a two-stage stochastic nonlinear programming problem. Ekonom.-Mat. Obzor, 14(3):322–330, 1978. [1890] Vlasta Kankovˇ a.´ Optimum solution of a stochastic optimization problem with unknown parameters. In Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions and the Eighth European Meeting of Statisticians (Tech. Univ. Prague, Prague, 1974), Vol. B, pages 239–244, Prague, 1978. Academia. [1891] Vlasta Kankovˇ a.´ Stability in the stochastic programming. Kybernetika (Prague), 14(5):339–349, 1978. [1892] Vlasta Kankovˇ a.´ Approximate solution of problems of two-stage stochastic nonlinear programming. Ekonom.-Mat. Obzor, 16(1):64–76, 1980. [1893] Vlasta Kankovˇ a.´ Optimization problem with parameter and its application to the problems of two- stage stochastic nonlinear programming. Kybernetika (Prague), 16(5):411–425, 1980. [1894] Vlasta Kankovˇ a.´ Sequences of stochastic programming problems with incomplete information. In Transactions of the ninth Prague conference on information theory, statistical decision functions, random processes, Vol. A (Prague, 1982), pages 327–332. Reidel, Dordrecht, 1983. [1895] Vlasta Kankovˇ a.´ Uncertainty in stochastic programming. In Stochastic optimization (Kiev, 1984), volume 81 of Lecture Notes in Control and Inform. Sci., pages 393–401. Springer, Berlin, 1986. [1896] Vlasta Kankovˇ a.´ Empirical estimates in stochastic programming. In Transactions of the Tenth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, Vol. B (Prague, 1986), pages 21–28. Reidel, Dordrecht, 1988. [1897] Vlasta Kankovˇ a.´ A note on the differentiability in two-stage stochastic nonlinear programming problems. Kybernetika (Prague), 24(3):207–215, 1988. [1898] Vlasta Kankovˇ a.´ Necessary and sufﬁcient optimality conditions for two-stage stochastic programming problems. Kybernetika (Prague), 25(5):375–385, 1989. [1899] Vlasta Kankovˇ a.´ A note on the minimax approach to the stochastic programming problems. Ekonom.-Mat. Obzor, 26(1):64–70, 1990. [1900] Vlasta Kankovˇ a.´ On the convergence rate of empirical estimates in chance constrained stochastic programming. Kybernetika (Prague), 26(6):449–461, 1990. [1901] Vlasta Kankova. A note on the stability in stochastic programming problems. In Information theory, statistical decision functions, random processes, Trans. 11th Prague Conf., Prague/Czech. 1990, Vol. B, 51-59, 1992. [1902] Vlasta Kankovˇ a.´ Stability in stochastic programming—the case of unknown location parameter. Kybernetika (Prague), 29(1):80–101, 1993. [1903] Vlasta Kankovˇ a.´ A note on estimates in stochastic programming. J. Comput. Appl. Math., 56(1- 2):97–112, 1994. Stochastic programming: stability, numerical methods and applications (Gosen, 1992).

107 [1904] Vlasta Kankovˇ a.´ A note on the relationship betweeen distribution function estimation and esti- mations in stochastic programming. In Trans. of the Twelfth Prague Conference, pages 122–125, 1994. [1905] Vlasta Kankovˇ a.´ On stability in two-stage stochastic nonlinear programming. In Asymptotic statistics (Prague, 1993), Contrib. Statist., pages 329–340. Physica, Heidelberg, 1994. [1906] Vlasta Kankovˇ a.´ On the stability in stochastic programming—generalized simple recourse problems. Informatica, 5(1-2):55–78, 1994. [1907] Vlasta Kankovˇ a.´ A note on contamination in stochastic programming – special cases, 1996. Kvan- titatívne metody´ v ekonomike (viackriterialna´ optimizacia´ VIII). Slov. spol. pre operacnˇ y´ vyzkum´ Bratislava. [1908] Vlasta Kankovˇ a.´ A note on interval estimates in stochastic optimization. Bulletin of the Czech Econometric Society, 5:63–79, 1996. [1909] Vlasta Kankovˇ a.´ A note on objective functions in multistage stochastic nonlinear programming problems. In System modelling and optimization (Prague, 1995), pages 582–589. Chapman & Hall, London, 1996. [1910] Vlasta Kankovˇ a.´ Convexity, Lipschitz property and differentiability in two-stage stochastic nonlinear programming problems. In Proceedings of the 3rd International Conference on Approximation and Optimization in the Caribbean (Puebla, 1995), page 17 pp. (electronic). Benemerita´ Univ. Auton.´ Puebla, Puebla, 1997. [1911] Vlasta Kankovˇ a.´ On an "-solution of minimax problem in stochastic programming. In J. Stˇ epˇ an´ V. Benes,ˇ editor, Proceedings of the 3rd International Conference on Distributions with Given Marginals and Moment Problems, pages 211–216, Dordrecht-Boston-London, 1997. Kluwer Aca- demic. Publisher. [1912] Vlasta Kankovˇ a.´ On estimates in time dependent stochastic optimization. Zeitschrift fur¨ Ange- wandte Mathematik und Mechanik, 77:587–588, 1997. [1913] Vlasta Kankovˇ a.´ On the stability in stochastic programming: the case of individual probability constraints. Kybernetika (Prague), 33(5):525–546, 1997. [1914] Vlasta Kankovˇ a.´ A note on empirical estimates and probability multifunctions in stochastic programming. In M. Huskovˇ a,´ P. Lachout, and J.A. Vísek,ˇ editors, Proceedings of the Conference Prague Stochastics ’98, pages 279–284, Prague, 1998. Union of Czech Mathematicians and Physi- cists. [1915] Vlasta Kankovˇ a.´ A note on multifunctions in stochastic programming. In Stochastic programming methods and technical applications (Neubiberg/Munich, 1996), pages 154–168. Springer, Berlin, 1998. [1916] Vlasta Kankovˇ a.´ Remarks on contamination in stochastic programming. Central European Journal for Operations Research and Economics, 6(3-4):215–224, 1998. [1917] Vlasta Kankovˇ a.´ A note on analysis of economic activities with random elements. In M. Plevny´ and V. Friedlich, editors, Proceedings of the Mathematical Methods in Economics 1998, pages 53–58, Cheb (Czech Republic), 1999. Vydavatelství Zapado´ ceskˇ e´ university. [1918] Vlasta Kankovˇ a.´ A note on multistage stochastic programming. In Proceedings of the 11th Joint Czech-German- Slovak Conference “Mathematical Methods in Economy and Industry”, pages 45– 52, Liberec (Czech Republic), 1999. Technicka´ univerzita Liberec, Vysokoskolskˇ y´ podnik. [1919] Vlasta Kankovˇ a.´ Multistage stochastic programming; stability, approximation and markov dependence. Operations Research Proceedings 1999, pages 136–141, 2000.

108 [1920] Vlasta Kankovˇ a.´ Multistage stochastic programming; stability, approximation and Markov dependence. In Operations Research Proceedings 1999 (Magdeburg), pages 136–141, Berlin, 2000. Springer. [1921] Vlasta Kankovˇ a.´ A remark on multiobjective stochastic optimization problems: stability and empirical estimates. In Operations Research Proceedings 2003, pages 379–386, Berlin, 2004. Springer. [1922] Vlasta Kankovˇ a´ and Petr Lachout. Convergence rate of empirical estimates in stochastic programming. Informatica, 3(4):497–523, 595, 603, 1992. [1923] Vlasta Kankovˇ a´ and Karel Sladky. Risk-sensitive optimality criteria in multistage stochastic optimization. In D. Bauerova,´ J. Hanclovˇ a,´ L. Hrbać,ˇ J. Mockoˇ r,ˇ and J. Ramík, editors, Proc. of the Mathematical Methods in Economics. Matematicke´ metody v ekonomii, Ostrava, pages 95–101. VSB,ˇ 1997. [1924] Vlasta Kankovˇ a´ and Martin Smˇ íd. On approximation in multistage stochastic programs: Markov dependence. Kybernetika (Prague), 40(5):625–638, 2004. [1925] R. Kannan. Stochastic approximation and nonlinear operator equations. In Approximate solution of random equations, pages 87–105, New York, 1979. North-Holland. [1926] Ravi Kannan, John Mount, and Sridhar Tayur. A randomized algorithm to optimize over certain convex sets. Math. Oper. Res., 20(3):529–549, 1995. [1927] A. Kanudia and R. Loulou. Robust responses to climate change via stochastic MARKAL: The case of Quebec. European Journal of Operational Research, 106(1):15–30, 1998. [1928] A. Kanudia and R. Loulou. Advanced bottom-up modelling for national and regional energy planning in response to climate change. International Journal of Environment and Pollution, 12(2– 3):191–216, 1999. [1929] A. Kanudia and P. R. Shukla. Modelling of uncertainties and price elastic demands in energy- environment planning for India. Omega-International Journal of Management Science, 26(3):409– 423, 1998. [1930] Chiang Kao and Shih-Pin Chen. A stochastic quasi-Newton method for simulation response optimization. European J. Oper. Res., 173(1):30–46, 2006. [1931] Edward P.C. Kao. A preference order dynamic program for stochastic assembly line balancing. Management Sci. 22, 1097-1104, 1976. [1932] Edward P.C. Kao and Maurice Queyranne. Aggregation in a two-stage stochastic program for manpower planning in the service sector. In Delivery of urban services, TIMS Stud. Manage. Sci. 22, 205-225, 1986. [1933] E.P.C. Kao and M. Queyranne. Budgeting cost of nursing in a hospital. Management Science, 31(5):608–621, 1985. [1934] Robert S. Kaplan and John V. Soden. On the objective function for the sequential P-model of chance-constrained programming. Operations Res. 19, 105-114, 1971. [1935] A.I. Kaplinskii and A.S. Krasnenker. The multitest approach to the formation of multilevel algorithms for stochastic optimization. Avtomat. i Vycisl.ˇ Tehn. (Riga), 4:14–21, 1975. [1936] A.I. Kaplinskii, A.S. Krasnenker, and A.V. Nazin. Training by the decrease principle in a vector optimization problem. Avtom. Vychisl. Tekh. 1978, No.4, 43-47, 1978. [1937] A.I. Kaplinskii, A.S. Krasnenker, and Ya. Z. Tsypkin. Randomization and smoothing in adaptation problems and algorithms. Automat. Remote Control, 35(6, part 1):913–921, 1974.

109 [1938] A.I. Kaplinskii, A.S. Poznjak, and A.I. Propoi. Optimality conditions for certain stochastic programming problems. Autom. Remote Control 1971, 1210-1218 translation from Avtom. Telemekh. 1971, No.8, 51-60 (1971)., 1972. [1939] A.I. Kaplinskii, A.S. Poznjak, and A.I. Propoi. Some methods for the solution of stochastic programming problems. Autom. Remote Control 32, 1609-1616 translation from Avtom. Telemekh. 1971, No.10, 87-94 (1971)., 1972. [1940] A.I. Kaplinskii and A.I. Propoi. Nonlocal optimization methods that use potential theory. Avtomat. i Telemekh., 7:55–65, 1993. [1941] A.I. Kaplinskii and A.I. Propoi. Second-order reﬁnement conditions in nonlocal optimization methods that use potential theory. Avtomat. i Telemekh., 8:104–117, 1994. [1942] A.I. Kaplinskij. Stochastic conditions for optimality. In Issled. Operacii. Modeli, Sist. Resen. 2. 1970, 119-124, 1971. [1943] A.I. Kaplinskij, A.S. Krasnenker, and A.V. Nazin. Training of convolution principle in vector optimization problems. Autom. Control Comput. Sci. 12, No.4, 41-45, 1978. [1944] A.I. Kaplinskij, A.E. Limarev, and G.D. Chernyshova. A construction of randomized optimization algorithms. Probl. Sluchajnogo Poiska 8, 63-91, 1980. [1945] A.I. Kaplinskij and A.M. Pesin. A method of construction of randomized algorithms. Autom. Re- mote Control 43, No.12, 1551-1559 translation from Avtom. Telemekh. 1982, No.12, 65-75 (1982)., 1983. [1946] A.I. Kaplinskij and A.I. Propoj. Stochastic approach to nonlinear programming problems. Automat. Remote Control 1970, 448-459 (970); translation from Avtomat. Telemekh. 1970, No.3, 122-133, 1970. [1947] V.A. Kardash. Stochastic, objectively-conditioned estimates of industrial factors. Optimizatsiya 34(51), 101-121, 1984. [1948] Uday S. Karmarkar. Convex/stochastic programming and multilocation inventory problems. Naval Res. Logist. Quart., 26(1):1–19, 1979. [1949] H.F. Karreman. Duality in stochastic programming applied to the design and operation of reser- voirs. In Recent results in stochastic programming (Proc. Meeting, Oberwolfach, 1979), volume 179 of Lecture Notes in Econom. and Math. Systems, pages 163–178. Springer, Berlin, 1980. [1950] G.V. Karumidze and V.G. Thinvaleli. Solution of a certain class of stochastic programming problems. Sakharth. SSR Mecn. Akad. Moambe, 67:565–568, 1972. [1951] A.N. Kashper and G.C. Varvaloucas. Trunk implementation plan for hierarchical networks. AT&T Bell Labs. Tech. J., 63(1):57–88, 1984. [1952] E.I. Kasitskaya. Approximation of the solution of a stochastic programming problem with noise that is a homogeneous random ﬁeld. In Mathematical decision-making methods under conditions of uncertainty (Russian), pages 23–27. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1990. [1953] E.I. Kasitskaya and P.S. Knopov. Asymptotic behaviour of empirical estimators in stochastic programming problems. Sov. Math., Dokl. 42, No.3, 751-753 translation from Dokl. Akad. Nauk SSSR 315, No.2, 279-281 (1990)., 1991. [1954] E.I. Kasitskaya and P.S. Knopov. Convergence of empirical estimates in stochastic optimization problems. Kibernetika (Kiev), 2:104–107, 112, 135, 1991. [1955] Aldona Katkauskaite.˙ Minimization algorithm in the presence of random noise. Informatica, 1(1):59–70, 186, 197, 1990.

110 [1956] Aldona Katkauskaite.˙ Minimization of functions that are observable with noise. Teor. Optimal. Reshenii, 14:78–92, 1990. [1957] Aldona Katkauskate.˙ An estimate of the parameters of a statistical model of global optimization. Teor. Optimal. Reshenii, 13:59–67, 1988. [1958] V. Ja. Katkovnik. The method of averaging operators in iteration algorithms for the solution of stochastic extremal problems. Kibernetika (Kiev), 4:123–131, 1972. [1959] V. Ja. Katkovnik. Iteration algorithms for random search in stochastic extremal problems. In Problems of random search, 2 (Russian), pages 31–42, 219. Izdat. “Zinatne”, Riga, 1973. [1960] V. Ja. Katkovnik and L.V. Ovcarova.ˇ Parametric statistical estimates in relay algorithms for random search. Avtomat. i Vycisl.ˇ Tehn. (Riga), 1:69–71, 1974. [1961] V.Ja. Katkovnik and L.V. Ovcarova. Konvergenz und Konvergenzgeschwindigkeit der Methode der parametrischen statistischen Gradienten. Kibernetika, Kiev 1974, Nr. 2, 115-118, 1974. [1962] V.Ja. Katkovnik and L.V. Ovcarova. Parametrical statistical evaluations in relay algorithms of random search. Avtomat. vycislit. Tehn., Riga 1974, Nr. 1, 69-71, 1974. [1963] V.Ja. Katkovnik and L.V. Ovcarova. Parametrische statistische Abschaetzungen in mehrstuﬁgen Algorithmen der zufaelligen Suche. Kibernetika, Kiev 1974, Nr. 3, 94-100, 1974. [1964] V.Ya. Katkovnik. Numerical Methods for Solving Deterministic and Stochastic Minimax Problems. Naukova dumka, Kiev, 1979. (in Russian). [1965] V.Ya. Katkovnik and V.E. Khejsin. Dynamic stochastic approximation of nonstationary solution of constrained extremum problem. Autom. Remote Control 41, 794-801 translation from Avtom. Telemekh. 1980, No.6, 70-79 (1980)., 1980. [1966] V.Ya. Katkovnik, O.Yu. Kul’chitskij, and V.E. Khejsin. Approximation of solutions of strongly nonstationary stochastic extremal problems in continuous time. I: Principles of design of algorithms. Autom. Remote Control 43, 1424-1431 translation from Avtom. Telemekh. 1982, No.11, 73-80 (1982)., 1983. [1967] Naoki Katoh. An -approximation scheme for minimum variance problems. J. Oper. Res. Soc. Japan, 33(1):46–65, 1990. [1968] I. Ya. Kats and G.A. Timofeeva. A bicriterial problem of stochastic optimization. Avtomat. i Telemekh., 3:116–123, 1997. [1969] Eliakim Katz. A note on a comparative statics theorem for choice under risk. J. Econ. Theory 25, 318-321, 1981. [1970] A. Kaufmann and R. Cruon. Strategies k-optimales dans les programmes dynamiques stochastiques ﬁnies. In Proc. 4th Int. Conf. Oper. Res., Boston 1966, 185-200, 1969. [1971] Hemanshu Kaul and Sheldon H. Jacobson. New global optima results for the Kauffman NK model: handling dependency. Math. Program., 108(2-3, Ser. B):475–494, 2006. [1972] Michal Kaut and Stein W. Wallace. Evaluation of scenario-generation methods for stochastic programming. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [1973] Michal Kaut and Stein W. Wallace. Shape-based scenario generation using copulas. Stochastic Programming E-Print Series, http://www.speps.org, 2006. [1974] Michal Kaut and Stein W. Wallace. Evaluation of scenario generation methods for stochastic programming. Pac. J. Optim., 3(2):257–271, 2007.

111 [1975] Ivan Kavkler and Alenka Kavkler. Stochastic linear optimization model (SLOM) using factor analysis. In Proceedings of the 10th International Conference on Operational Research—KOI 2004, pages 111–119. Univ. Osijek Dep. Math., Osijek, 2005. [1976] V.V. Kazakevicˇ and I.A. Mocalov.ˇ Sequential algorithm for accelerated search for the extremum in inertial optimization objects. Dokl. Akad. Nauk SSSR, 226(1):77–80 (1 plate), 1976. [1977] V.V. Kazakevich, I.A. Mochalov, and L.B. Prigozhin. Optimization of measurements in accelerated algorithms of extremal control. Autom. Remote Control 47, 1217-1226 translation from Avtom. Telemekh. 1986, No.9, 60-69 (1986)., 1986. [1978] A. Kekhajov. A minimum required number of statistical tests for one class of simulation models. Avtom. Izchislitelna Tekh. 15, No.2, 47-53, 1981. [1979] P. Kelle. Chance constrained inventory model for an asphalt mixing problem. In Recent results in stochastic programming (Proc. Meeting, Oberwolfach, 1979), volume 179 of Lecture Notes in Econom. and Math. Systems, pages 179–189, Berlin, 1980. Springer. [1980] Peter Kelle. Stochastic programming models for safety stock allocation. In Stochastic optimization, Proc. Int. Conf., Kiev/USSR 1984, Lect. Notes Control Inf. Sci. 81, 402-411, 1986. [1981] C.M. Keller, A.V. Cabot, and B.G. Flury. Two algorithms for global optimization. Math. Comput. Modelling, 21(12):47–59, 1995. [1982] D.G. Kelly and J.W. Tolle. Expected number of vertices of a random convex polyhedron. SIAM J. Algebraic Discrete Methods, 2(4):441–451, 1981. [1983] J. Kelman, J. R. Stedinger, L. A. Cooper, E. Hsu, and S-U. Yuan. Sampling stochastic dynamic programming applied to reservoir operations. Water Resources Research, 26:447–454, 1990. [1984] R. Kelman, L. A. N. Barroso, and M. V. F. Pereira. Market power assessment and mitigation in hydrothermal systems. IEEE Transactions on Power Systems, 16(3):354–359, 2001. [1985] Milton L. Kelmanson and Priscila Goldenberg. A convergent “small steps” feasible directions stochastic approximation algorithm. In Third Symposium on Operations Research (Univ. Mannheim, Mannheim, 1978), Section 3, volume 33 of Operations Res. Verfahren, pages 247–259. Hain, Konigstein/Ts.,¨ 1979. [1986] D.P. Kennedy. Stimulating prices in a stochastic model of resource allocation. Math. Oper. Res. 8, 151-157, 1983. [1987] D.P. Kennedy. Optimal sequential assignment. Math. Oper. Res., 11(4):619–626, 1986. [1988] A.S. Kenyon and D.P. Morton. Stochastic vehicle routing with random travel times. Transportation Science, 37:69–82, 2003. [1989] Astrid S. Kenyon and David P. Morton. A survey on stochastic location and routing problems. CEJOR Cent. Eur. J. Oper. Res., 9(4):277–328, 2001. [1990] C. M. Kenyon, S. Savage, and B. Ball. Equivalence of linear deviation about the mean and mean absolute deviation about the mean objective functions. Oper. Res. Lett., 24(4):181–185, 1999. [1991] G. Keri. On the two-stage programming under uncertainty. Stud. Sci. Math. Hungar. 5, 37-40, 1970. [1992] B. P. Kharlamov. Semi-Markov processes for ﬁnding a maximum. Avtomat. i Telemekh., (9):97– 111, 2000. [1993] Lov Kumar Kher and Soroosh Sorooshian. A predictive demand model for systems planning, using noisy realization theory. Automatica 24, No.5, 671-676, 1988.

112 [1994] I.L. Khranovich. Simulation of optimal development for water-supply systems. II: A flow approach. Autom. Remote Control 45, 1346-1353 translation from Avtom. Telemekh. 1984, No.10, 121-130 (1984)., 1984. [1995] V.N. Khrapko. Full-step relaxation algorithms for stochastic programming. In Dynamic systems, No. 2, pages 97–102. “Vishcha Shkola”, Kiev, 1983. [1996] V.M. Kibardin. Decomposition into functions in the minimization problem. Automat. Remote Control, 40(9, part 1):1311–1323 (1980), 1979. [1997] A. I. Kibzun and E. A. Kuznetsov. Convex properties of the quantile function in stochastic programming problems. Avtomat. i Telemekh., (2):33–42, 2004. [1998] A. I. Kibzun and I. V. Nikulin. Discrete approximation of a linear two-stage stochastic programming problem with a quantile criterion. Avtomat. i Telemekh., (8):127–137, 2001. [1999] A. I. Kibzun and G. L. Tretyakov. On the smoothness of the criterial function in the quantile optimization problem. Avtomat. i Telemekh., 9:69–80, 1997. [2000] A.I. Kibzun and Y.S. Kan. Stochastic Programming Problems with Probability and Quantile Func- tions. Wiley, Chichester, 1996. [2001] A.I. Kibzun and V.Yu. Kurbakovskij. Guaranteeing approach to solving quantile optimization problems. Ann. Oper. Res. 30, 81-93, 1991. [2002] A.I. Kibzun, A.A. Lebedev, and V.V. Malyshev. Reduction of an optimization problem with probabilistic constraints to an equivalent minimax problem. Soviet J. Comput. Systems Sci., 23(1):39–47, 1985. [2003] A.I. Kibzun and V.V. Malyshev. Generalized minimax approach to solving optimization problems with chance constraints. Engrg. Cybernetics, 22(1):105–114 (1985), 1984. [2004] A.I. Kibzun and V.V. Malyshev. Optimal control of a discrete-time stochastic system. Sov. J. Comput. Syst. Sci. 24, No.2, 69-77 translation from Izv. Akad. Nauk SSSR, Tekh. Kibern. 1985, No.6, 113-120 (1985)., 1986. [2005] A.I. Kibzun and V.V. Malyshev. Probabilistic optimization problems. Sov. J. Comput. Syst. Sci. 28, No.4, 52-60 translation from Izv. Akad. Nauk SSSR, Tekh. Kibern. 1989, No.6, 46-55 (1989)., 1990. [2006] A.I. Kibzun and A.V. Naumov. Two-stage problems of quantile linear programming. Avtomat. i Telemekh., 1:83–93, 1995. [2007] Andrey Kibzun and Riho Lepp. Discrete approximation in quantile problem of portfolio selection. In Stochastic optimization: algorithms and applications (Gainesville, FL, 2000), volume 54 of Appl. Optim., pages 121–135. Kluwer Acad. Publ., Dordrecht, 2001. [2008] Masaaki Kijima and Masamitsu Ohnishi. Stochastic orders and their applications in financial optimization. Math. Methods Oper. Res., 50(2):351–372, 1999. Financial optimization. [2009] Masaaki Kijima and Akihisa Tamura. On the greedy algorithm for stochastic optimization problems. In Stochastic modelling in innovative manufacturing (Cambridge, 1995), volume 445 of Lecture Notes in Econom. and Math. Systems, pages 19–29. Springer, Berlin, 1997. [2010] Hyong Sop Kim. A computational procedure of the stochastic programming problem. Cho-son In-min Kong-hwa-kuk Kwa-hak-won T’ong-bo, 4:39–43, 1982. [2011] Joocheol Kim. Estimation of optimality gap using stratified sampling. Appl. Math. Comput., 171(2):710–720, 2005.

113 [2012] Tae-ho Kim and Soon Dal Park. A decomposition method for two stage stochastic programming with block diagonal structure. J. Korean Oper. Res. Manage. Sci. Soc. 10, No.1, 9-13, 1985. [2013] Yong Kim. Convergence of a generalized gradient descent algorithm for limit extremal problems. Su-hak, 3:22–24, 1995. [2014] A.J. King. An implementation of the Lagrangian ﬁnite-generation method. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 295–311. Springer, Berlin, 1988. [2015] A.J. King. Stochastic programming problems: examples from the literature. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 543–567. Springer, Berlin, 1988. [2016] A.J. King, editor. Approximation and computation in stochastic programming. North-Holland Publishing Co., Amsterdam, 1996. Math. Programming 75 (1996), no. 2, Ser. B, see also Erratum in Math. Programming 80 (1998), no. 1, Ser. A. [2017] A.J. King, R.T. Rockafellar, L. Somlyody, and R.J.-B. Wets. Lake eutrophication management: The Lake Balaton project. In Numerical techniques for stochastic optimization, Springer Ser. Comput. Math. 10, 435-444, 1988. [2018] A.J. King and R.J.-B. Wets. Erratum: “Epi-consistency of convex stochastic programs”. Stochastics Stochastics Rep., 37(4):259–260, 1991. [2019] Alan King and Lisa Korf. Martingale pricing measures in incomplete markets via stochastic programming duality in the dual of L∞. Stochastic Programming E-Print Series, http: //www.speps.org, 2001. [2020] Alan J. King. Asymmetric risk measures and tracking models for portfolio optimization under uncertainty. Ann. Oper. Res. 45, No.1-4, 165-177, 1993. [2021] Alan J. King. Duality and martingales: a stochastic programming perspective on contingent claims. Math. Program., 91(3, Ser. B):543–562, 2002. ISMP 2000, Part 1 (Atlanta, GA). [2022] Alan J. King, Matti Koivu, and Teemu Pennanen. Calibrated option bounds. Stochastic Program- ming E-Print Series, http://www.speps.org, 2003. [2023] Alan J. King and R. Tyrrell Rockafellar. Asymptotic theory for solutions in statistical estimation and stochastic programming. Math. Oper. Res., 18(1):148–162, 1993. [2024] Alan J. King, Laszl´ o´ Somlyody,´ and Roger J.-B. Wets. Stochastic optimization for lake eutrophication management. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 347–378. SIAM, Philadelphia, PA, 2005. [2025] Alan J. King, Samer Takriti, and Shabbir Ahmed. Issues in risk modeling for multi-stage systems. Ibm research report rc 20993, IBM Research Division, T.J. Watson Research Center, Yorktown Heights, New York, 1997. [2026] Alan J. King and Roger J.-B. Wets. Epi-consistency of convex stochastic programs. Stochastics Stochastics Rep., 34(1-2):83–92, 1991. [2027] Alan J. King, Stephen E. Wright, Gyana R. Parija, and Robert Entriken. The IBM stochastic programming system. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 21–36. SIAM, Philadelphia, PA, 2005. [2028] M.J.L. Kirby. The current state of chance-constrained programming. In Proceedings of the Prince- ton Symposium on Mathematical Programming (Princeton, 1967), pages 93–111, Princeton, N.J., 1970. Princeton Univ. Press.

114 [2029] Scott Kirkpatrick. Optimization by simulated annealing: quantitative studies. J. Statist. Phys., 34(5-6):975–986, 1984. [2030] V.P. Kirlitsa. On a stochastic programming problem with linear decision rules. Vestn. Beloruss. Gos. Univ. Im. V. I. Lenina, Ser. I 1983, No.1, 35-37, 1983. [2031] V.P. Kirlitsa. A problem of linear stochastic programming with two-sided constraints. Vestnik Beloruss. Gos. Univ. Ser. I, 1:33–36, 79, 1985. [2032] V.P. Kirlitsa and A. Casado. On a problem of stochastic linear programming with nondeterministic constraint matrix. Investigacion´ Oper., 27:3–8, 1979. [2033] V.P. Kirlitsa and Rosa Vazquez.´ On a problem of stochastic linear programming with two-sided constraints. Investigacion´ Oper., 27:9–16, 1979. [2034] V.P. Kirlitza and Alfonso Casado Collado. On a problem of stochastic linear programming. Inves- tigacion´ Oper., 1(1):27–33, 1980. [2035] V.P. Kirlitza and Alfonso Casado Collado. On the problem of linear stochastic programming with the uniform distribution. Investigacion´ Oper., 3(2):41–50, 1982. [2036] N.I. Kiselev. Linear programming in extremal problems of statistics. In Statistics. Probability. Economics, volume 49 of Uchen. Zap. Statist., pages 31–39. “Nauka”, Moscow, 1985. [2037] V.G. Kiselev. Approximation of probability constraints in some production planning problems. U.S.S.R. Comput. Math. Math. Phys. 23, No.1, 56-63 translation from Zh. Vychisl. Mat. Mat. Fiz. 23, No.1, 83-94 (1983)., 1983. [2038] E. M. Kiseleva and K. A. Kuznetsov. On the solution of the continuous stochastic problem of optimal partitioning with reconstruction of the objective function. Problemy Upravlen. Inform., 151(6):81–88, 1998. [2039] E.M. Kiseleva and N.Z. Shor. The solution of the continuous optimal decomposition problem with incomplete initial data. Comput. Math. Math. Phys. 31, No.6, 13-20 translation from Zh. Vychisl. Mat. Mat. Fiz. 31, No.6, 799-809 (1991)., 1991. [2040] K.C. Kiwiel, C.H. Rosa, and A. Ruszczynski.´ Decomposition via alternating linearization. Working paper WP-95-051, IIASA, Laxenburg, 1995. [2041] Krzysztof C. Kiwiel. Proximal minimization methods with generalized Bregman functions. SIAM J. Control Optim., 35(4):1142–1168, 1997. [2042] Krzysztof C. Kiwiel, Charles H. Rosa, and Andrzej Ruszczynski.´ Proximal decomposition via alternating linearization. SIAM J. Optim., 9(3):668–689, 1999. [2043] G. Kjellstroem and L. Taxen. Gaussian adaptation, an evolution-based efﬁcient global optimizer. In Computational and applied mathematics, I. Algorithms and theory, Sel. Rev. Pap. IMACS 13th World Congr., Dublin/Irel. 1991, 267-276, 1992. [2044] Gregor Kjellstrom¨ and Lars Taxen.´ Stochastic optimization in system design. IEEE Trans. Circuits and Systems, 28(7):702–715, 1981. [2045] Hans-Siegfried Klausmann. Stochastische Entscheidungsbaume¨ . Verlag Anton Hain, Meisenheim am Glan, 1976. Ein Beitrag zur Losung¨ von sequentiellen Entscheidungsproblemen bei Risiko, Mit einem Vorwort von M. Meyer, Beitrage¨ zur Datenverarbeitung und Unternehmensforschung, Band 18. [2046] G. Klein, H. Moskowitz, and A. Ravindran. Interactive multiobjective optimization under uncertainty. Management Sci., 36(1):58–75, 1990.

115 [2047] Willem K. Klein Haneveld. Duality in stochastic linear and dynamic programming, volume 274 of Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin, 1986. [2048] Willem K. Klein Haneveld. Robustness against dependence in PERT: An application of duality and distributions with known marginals. Math. Program. Study 27, 153-182, 1986. [2049] Willem K. Klein Haneveld, Leen Stougie, and Maarten H. van der Vlerk. On the convex hull of the simple integer recourse objective function. Ann. Oper. Res., 56:209–224, 1995. Stochastic programming (Udine, 1992). [2050] Willem K. Klein Haneveld, Leen Stougie, and Maarten H. van der Vlerk. An algorithm for the construction of convex hulls in simple integer recourse programming. Ann. Oper. Res., 64:67–81, 1996. Stochastic programming, algorithms and models (Lillehammer, 1994). [2051] Willem K. Klein Haneveld, Leen Stougie, and Maarten H. van der Vlerk. Simple integer recourse models. Stochastic Programming E-Print Series, http://www.speps.org, 2005. [2052] Willem K. Klein Haneveld, Leen Stougie, and Maarten H. van der Vlerk. Simple integer recourse models: convexity and convex approximations. Math. Program., 108(2-3, Ser. B):435–473, 2006. [2053] Willem K. Klein Haneveld and Maarten H. van der Vlerk. On the expected value function of a simple integer recourse problem with random technology matrix. J. Comput. Appl. Math., 56(1- 2):45–53, 1994. Stochastic programming: stability, numerical methods and applications (Gosen, 1992). [2054] Willem K. Klein Haneveld and Maarten H. van der Vlerk. Stochastic integer programming: general models and algorithms. Ann. Oper. Res., 85:39–57, 1999. Stochastic programming. State of the art, 1998 (Vancouver, BC). [2055] Willem K. Klein Haneveld and Maarten H. van der Vlerk. Optimizing electricity distribution using two-stage integer recourse models. In Stochastic optimization: algorithms and applications (Gainesville, FL, 2000), volume 54 of Appl. Optim., pages 137–154. Kluwer Acad. Publ., Dor- drecht, 2001. [2056] Willem K. Klein Haneveld and Maarten H. van der Vlerk. Integrated chance constraints: reduced forms and an algorithm. Comput. Manag. Sci., 3(4):245–269, 2006. [2057] W.K. Klein Haneveld. Some linear programs in probabilities and their duals. In Convexity and duality in optimization (Groningen, 1984), volume 256 of Lecture Notes in Econom. and Math. Systems, pages 95–141, Berlin, 1985. Springer. [2058] W.K. Klein Haneveld. On integrated chance constraints. In Stochastic programming (Gargnano, 1983), volume 76 of Lecture Notes in Control and Inform. Sci., pages 194–209. Springer, Berlin, 1986. [2059] W.K. Klein Haneveld, L. Stougie, and M.H. van der Vlerk. Stochastic integer programming with simple recourse. Research Memorandum 455, Institute of Economic Research, University of Groningen, 1991. [2060] W.K. Klein Haneveld, L. Stougie, and M.H. van der Vlerk. On the convex hull of the composition of a separable and a linear function. Discussion Paper 9570, CORE, Louvain-la-Neuve, Belgium, 1995. [2061] W.K. Klein Haneveld, L. Stougie, and M.H. van der Vlerk. Convex approximations for simple integer recourse models by perturbing the underlying distribution. Research Report 97A19, SOM, University of Groningen, 1997. [2062] W.K. Klein Haneveld, L. Stougie, and M.H. van der Vlerk. Convex simple integer recourse models. Research Report 97A10, SOM, University of Groningen, 1997.

116 [2063] W.K. Klein Haneveld, M.H. Streutker, and M.H. van der Vlerk. An ALM model for pension funds using integrated chance constraints. Research Report 05A03, SOM, University of Groningen, 2005. Revision of 03A21. [2064] W.K. Klein Haneveld, M.H. Streutker, and M.H. van der Vlerk. Modeling ALM for dutch pension funds. In J. Safrankova and J. Pavlu, editors, WDS’06 Proceedings of Contributed Papers: Part I - Mathematics and Computer Sciences, pages 100–105, Prague, 2006. Matfyzpress. [2065] W.K. Klein Haneveld and M.H. van der Vlerk. Optimizing electricity distribution using two-stage integer recourse models. In S. Uryasev and P.M. Pardalos, editors, Stochastic Optimization: Algo- rithms and Applications, pages 137–154. Kluwer Academic Publishers, 2001. [2066] W.K. Klein Haneveld and M.H. van der Vlerk. Stochastic Programming (Lecture Notes). Available on request, e-mail [email protected], 2007. [2067] N. L. Kleinman. Stochastic approximation algorithms: theory and applications. Ph.D. thesis, Dept. of Mathematical Sciences, The Johns Hopkins University, 1996. [2068] N.L. Kleinman, S.D. Hill, and V.A. Ilenda. SPSA/SIMMOD optimization of air trafﬁc delay cost. In Proceedings of the American Control Conference, pages 1121–1125, 1997. [2069] N.L. Kleinman, J.C. Spall, and D.Q. Naiman. Simulation-based optimization with stochastic approximation using common random numbers. Management Science, 45:1570–1578, 1999. [2070] Anton J. Kleywegt and Jason D. Papastavrou. The dynamic and stochastic knapsack problem. Oper. Res., 46(1):17–35, 1998. [2071] Anton J. Kleywegt and Jason D. Papastavrou. The dynamic and stochastic knapsack problem with random sized items. Oper. Res., 49(1):26–41, 2001. [2072] Anton J. Kleywegt, Alexander Shapiro, and Tito Homem-de Mello. The sample average approximation method for stochastic discrete optimization. SIAM J. Optim., 12(2):479–502 (electronic), 2001/02. [2073] Allen Klinger and O.L. Mangasarian. Logarithmic convexity and geometric programming. J. math. Analysis Appl. 24, 388-408, 1968. [2074] Rolf Kloetzler. Dualitaet und Fehlerabschaetzungen bei stochastischer diskreter dynamischer Op- timierung. Seminarber., Humboldt-Univ. Berlin, Sekt. Math. 39, 114-124, 1981. [2075] Leszek Klukowski. Some probabilistic properties of the nearest adjoining order method and its extensions. Ann. Oper. Res., 51:241–261, 1994. Support for decision and negotiation processes (Warsaw, 1992). [2076] Leonhard Knauff. Ein Programm zur Parameterschatzung¨ in nichtlinearen Modellen. Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe, 34(1):149–152, 1985. [2077] Charles S. Knode and Lloyd A. Swanson. A stochastic model for bidding. J. Oper. Res. Soc. 29, 951-957, 1978. [2078] P. S. Knopov and E. I. Kasitskaya. On large deviations of empirical estimates in stochastic programming problems. Kibernet. Sistem. Anal., 40(4):52–60, 189, 2004. [2079] P. S. Knopov and E. I. Kasitskaya. On the convergence of empirical estimates in stochastic programming problems in discrete-time processes. Kibernet. Sistem. Anal., 41(1):175–178, 191, 2005. [2080] Pavel S. Knopov and Evgeniya J. Kasitskaya. Empirical estimates in stochastic optimization and identiﬁcation, volume 71 of Applied Optimization. Kluwer Academic Publishers, Dordrecht, 2002.

117 [2081] P.S. Knopov. Remarks on the minimization of nondifferentiable functions. Kibernetika (Kiev), 2:44–45, 1975. [2082] P.S. Knopov. Weak convergence of measures generated by iterative procedures in Hilbert space. Dokl. Akad. Nauk SSSR, 256(1):29–32, 1981. [2083] P.S. Knopov. An approach to solving problems of stochastic optimization. Kibernetika (Kiev), 4:126–127, 136, 1988. [2084] P.S. Knopov and E.J. Kasitskaya. Properties of empirical estimates in stochastic optimization and identiﬁcation problems. Ann. Oper. Res., 56:225–239, 1995. Stochastic programming (Udine, 1992). [2085] M. Knott. Randomized decisions in chance-constrained programming. J. Oper. Res. Soc. 36, 959- 961, 1985. [2086] M.I. Koch, D.C. Chin, and R.H. Smith. Network-wide approach to optimal signal light timing for integrated transit vehicle and trafﬁc operations. In Proceedings of the 7th National Conference on Light Rail Transit, volume 2, pages 126–131. National Academy of Sciences Press, 1997. [2087] A.I. Kochubinskii. Recognition of pulse packets under conditions of incomplete information. Dokl. Akad. Nauk Ukrain. SSR Ser. A, 12:56–58, 86, 1988. [2088] U. Kockelkorn. Ein linearen Mehrentscheidungsmodell. Metrika 26, 169-182, 1979. [2089] Gerald Koenke. Lineare und stochastische Optimierung mit dem PC. (Linear and stochastic optima with the PC). Mikro-Computer-Praxis. Stuttgart: B. G. Teubner. 157 S., 1987. [2090] Konstantin Kogan, Eugene Khmelnitsky, and Toshihide Ibaraki. Dynamic generalized assignment problems with stochastic demands and multiple agent-task relationships. J. Global Optim., 31(1):17–43, 2005. [2091] Matti Koivu. Variance reduction in sample approximations of stochastic programs. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [2092] Matti Koivu. Variance reduction in sample approximations of stochastic programs. Math. Pro- gram., 103(3, Ser. A):463–485, 2005. [2093] M.A. Kokorev. Construction of a stochastic algorithm, optimal for one step, for the approximation of a Lipschitz function. Zh. Vychisl. Mat. i Mat. Fiz., 30(5):652–662, 798, 1990. [2094] V.V. Kolbin. Stochastische Programmierung. In Itogi Nauki, Ser. Mat., Teor. Verojatn., mat. Statist., teor. Kibernet. 1968, 5-68, 1970. [2095] V.V. Kolbin. Stochastic programming. In Progress Math. 11, 1-75, 1971. [2096] V.V. Kolbin. Stochastic programming. Theory and Decision Library. Vol. 14. Dordrecht - Boston: D. Reidel Publishing Company, 1977. Translated from Russian by Igor P. Grigoryev. [2097] Waldemar Kolodziejczyk. On equivalence of two optimization methods for fuzzy discrete programming problems. Eur. J. Oper. Res. 36, No.1, 85-91, 1988. [2098] Michael Kolonko. Uniform bounds for a dynamic programming model under adaptive control using exponentially bounded error probabilities. In Mathematical learning models—theory and algorithms (Bad Honnef, 1982), volume 20 of Lecture Notes in Statist., pages 108–114. Springer, New York, 1983. [2099] E. Komaromi. A dual approach to stochastic linear programming problems constrained by logarithmic concave joint probability distribution function. Alkalmazott Mat. Lapok 9, 85-92, 1983.

118 [2100] E.´ Komaromi.´ A dual method for probabilistic constrained problems. Math. Programming Stud., 28:94–112, 1986. Stochastic programming 84. II. [2101] E.´ Komaromi.´ On properties of the probabilistic constrained linear programming problem and its dual. J. Optim. Theory Appl., 55(3):377–390, 1987. [2102] E.´ Komaromi.´ Probabilistic constraints in primal and dual linear programs: duality results. J. Optim. Theory Appl., 75(3):587–602, 1992. [2103] Eva´ Komaromi.´ Actual approach to stochastic linear programming problems constrained by logarithmic concave joint probability distribution function. Alkalmaz. Mat. Lapok, 9(1-2):85–92, 1983. [2104] Eva´ Komaromi.´ Duality in probabilistic constrained linear programming. In System modelling and optimization (Budapest, 1985), volume 84 of Lecture Notes in Control and Inform. Sci., pages 423–429. Springer, Berlin, 1986. [2105] Eva´ Komaromi.´ On the convergence of a dual algorithm for the solution of the probabilistic constrained linear programming problem. Alkalmaz. Mat. Lapok, 14(1-2):85–98, 1989. [2106] S.V. Komolov, S.P. Makeev, G.P. Serov, and I.F. Shakhnov. Optimal control of a ﬁnite automaton with fuzzy constraints and a fuzzy target. Cybernetics, 15(6):805–810 (1980), 1979. [2107] Nan Kong, Andrew Schaefer, and Shabbir Ahmed. Totally unimodular stochastic programs. Opti- mization Online, http://www.optimization-online.org, 2006. [2108] Nan Kong and Andrew J. Schaefer. A factor 1/2 approximation algorithm for a class of two- stage stochastic mixed-integer programs. Stochastic Programming E-Print Series, http://www. speps.org, 2004.

1 [2109] Nan Kong and Andrew J. Schaefer. A factor 2 approximation algorithm for two-stage stochastic matching problems. European J. Oper. Res., 172(3):740–746, 2006. [2110] Nan Kong, Andrew J. Schaefer, and Brady Hunsaker. Two-stage integer programs with stochastic right-hand sides. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [2111] Ger Koole. Stochastic scheduling with event-based dynamic programming. Math. Methods Oper. Res., 51(2):249–261, 2000. [2112] Charles Kooperberg and Charles J. Stone. Stochastic optimization methods for fitting polyclass and feed-forward neural network models. J. Comput. Graph. Statist., 8(2):169–189, 1999. [2113] Jozef Kopec and Bogdan Krawiec. Application of model ”P” in a plant production optimization problem. Przegl. Stat. 29, 551-558, 1982. [2114] Lisa A. Korf. A finite-dimensional approach to infinite-dimensional constraints in stochastic programming duality. In Stochastic optimization: algorithms and applications (Gainesville, FL, 2000), pages 155–167. Kluwer Acad. Publ., Dordrecht, 2001. [2115] Lisa A. Korf. Stochastic programming duality: L∞ multipliers with an application to mathematical finance. Stochastic Programming E-Print Series, http://www.speps.org, 2001. [2116] Lisa A. Korf. Stochastic programming duality: L∞ multipliers for unbounded constraints with an application to mathematical finance. Math. Program., 99(2, Ser. A):241–259, 2004. [2117] Lisa A. Korf and Roger J.-B. Wets. An ergodic theorem for stochastic programming problems. In Optimization (Namur, 1998), pages 203–217. Springer, Berlin, 2000. [2118] Lisa A. Korf and Roger J.-B. Wets. Random lsc functions: An ergodic theorem. Stochastic Pro- gramming E-Print Series, http://www.speps.org, 2000.

119 [2119] Lisa A. Korf and Roger J.-B. Wets. Random lsc functions: Scalarization. Stochastic Programming E-Print Series, http://www.speps.org, 2000. [2120] Lisa A. Korf and Roger J.-B. Wets. Random-lsc functions: an ergodic theorem. Math. Oper. Res., 26(2):421–445, 2001. [2121] A.S. Korkhin. Some properties of estimates for regression parameters with a priori inequality constraints. Kibernetika (Kiev), 6:iv, 106–114, 1985. [2122] J.S.H. Kornbluth. Duality, indifference and sensitivity analysis in multiple objective linear programming. Operat. Res. Quart. 25, 599-614, 1974. [2123] J. Koronacki. On the convergence of minimization algorithms in problems described by stochastic equations. In 18. internat. wiss. Kolloqu., Ilmenau 1, 51-53, 1973. [2124] Ja. Koronacki. The convergence of random search algorithms. Avtomat. i Vycisl.ˇ Tehn. (Riga), 4:43–49, 92, 1976. [2125] Jacek Koronacki. A stochastic approximation counterpart of the feasible direction method. Statist. Probab. Lett., 5(6):415–419, 1987. [2126] A.P. Korostelev. Multistep procedures of stochastic optimization. Autom. Remote Control 42, No.5, 621-628 translation from Avtom. Telemekh. 1981, No.5, 82-90 (1981)., 1981. [2127] A.P. Korostelev and E.A. Kitaev. Comparison of asymptotic behaviour of stochastic approximation and random search procedures. Avtom. Vychisl. Tekh. 1977, No.6, 37-38, 1977. [2128] K.O. Kortanek. Semi-inﬁnite programming duality for order restricted statistical inference models. Z. Oper. Res., 37(3):285–301, 1993. [2129] J. Korycki. On a distributed implementation of a decomposition method for multistage linear stochastic programs. Optimization, 38(2):173–200, 1996. [2130] Bernd Kost. Structural design via evolution strategies. In Stochastic programming (Neu- biberg/Munchen,¨ 1993), volume 423 of Lecture Notes in Econom. and Math. Systems, pages 71–92. Springer, Berlin, 1995. [2131] L.P. Kostina. A method for solving the optimal resource allocation problem on stochastic networks with a complex space-time structure. Vestnik S.-Peterburg. Univ. Mat. Mekh. Astronom., 3:36–43, 116–117, 1992. [2132] Vassilis S. Kouikoglou and Yannis A. Phillis. Minimax design of two-state k-out-of-n systems. Appl. Stochastic Models Data Anal., 9(3):245–250, 1993. [2133] R. Kouwenberg. Scenario generation and stochastic programming models for asset liability management. European Journal of Operational Research, 134(2):279–292, 2001. [2134] I.N. Kovalenko. Probabilistic Calculation and Optimization. Naukova dumka, Kiev, 1989. (in Russian). [2135] I.N. Kovalenko, N.Yu. Kuznetsov, and A.N. Nakonechnyj. Optimization of the characteristics of the reliability of systems on the basis of using qualitative estimates of continuity and methods of ac- celerate modeling. In Zolotarev, V. M. (ed.) et al., Stability problems of stochastic models. Seminar proceedings, Sukhumi (USSR), October 1987. Moskva: Vsesoyuznyj Nauchno-Issledovatel’skij In- stitut Sistemnykh Issledovanij, Probl. Ustojch. Stokhasticheskikh Modelej, Tr. Semin. 79-84, 1988. [2136] I.N. Kovalenko and A.N. Nakonechnyj. Approximate calculation and optimization of reliability. (Priblizhennyj raschet i optimizatsiya nadezhnosti). Naukova Dumka, Kiev, 1989.

120 [2137] M.M. Kovalev and V.A. Pir’yanovich. Locally stochastic algorithms of discrete optimization (experiments and computational experience). Cybernetics, 18(1):127–132, 1982. [2138] S.V. Kovalev and V.V. Mazalov. A risk function in global optimization problem. In Probabilistic methods in discrete mathematics (Petrozavodsk, 1992), volume 1 of Progr. Pure Appl. Discrete Math., pages 266–270. VSP, Utrecht, 1993. [2139] S.V. Kovalev and V.V. Mazalov. The risk function in the problem of the design of an experiment. In Modeling of natural systems and optimal control problems (Russian) (Chita), pages 83–92. VO “Nauka”, Novosibirsk, 1993. [2140] P. Kovanic and R.A. Barack. Robust survival model as an optimization problem. In System modelling and optimization (Compiegne,` 1993), volume 197 of Lecture Notes in Control and Inform. Sci., pages 375–382. Springer, London, 1994. [2141] Andrzej Koziarski. Application of the stochastic subgradient method for long-term planning of the state of a dynamic plant operating in the presence of random disturbances. Arch. Automat. Telemech., 25(4):507–517 (1981), 1980. [2142] O. Krafft. Dual optimization problems in stochastics. Jahresber. Deutsch. Math.-Verein., 83(3):97– 105, 1981. [2143] W.F Krajewski. The sequential problem under uncertainty. The development of water systems. Comput. Math. Appl, 8:313–318, 1982. [2144] A.S. Krasnenker. The method of local improvements in the vector-optimization problem. Autom. Remote Control 36, 419-422 translation from Avtom. Telemekh. 1975, No.3, 75-79 (1975)., 1975. [2145] A.A. Krasovskii. Continuous algorithms and the stochastic dynamics of searching for an extremum. Avtomat. i Telemekh., 4:55–65, 1991. See also Erratum, ibid. 10:189, 1991. [2146] A.N. Krasovskij. Control under minimax of an integral functional. Sov. Math., Dokl. 44, No.2, 525-528 translation from Dokl. Akad. Nauk SSSR 320, No.4, 785-788 (1991)., 1992. [2147] N.N. Krasovskij. A minimax control problem. Differ. Equations 18, 1511-1517 translation from Differ. Uravn. 18, No.12, 2126-2132 (1982)., 1983. [2148] N.N. Krasovskij. Control with deﬁcit of information. Sov. Math., Dokl. 31, 108-112 translation from Dokl. Akad. Nauk SSSR 280, 536-540 (1985)., 1985. [2149] N.N. Krasovskij and V.E. Tret’yakov. A stochastic program synthesis of a guaranteeing control. Probl. Control Inf. Theory 12, 79-95 (Russian. English translation enclosed), 1983. [2150] L.V. Kravtsova, Ya. D. Plotkin, and L.G. Smyshlyaeva. On the theory of optimization with respect to a probability criterion and its use in calculating the output percentage of nondefective semi- conductor devices. In Partial differential equations (Russian), pages 70–79. “Obrazovanie”, St. Petersburg, 1992. [2151] Jacek B. Krawczyk. On variance constrained programming. Asia-Paciﬁc J. Oper. Res., 7(2):190– 208, 1990. [2152] L.I. Krechetov. Necessary conditions of optimality with constraints which are valid “almost every- where” with respect to a controlled measure. In Studies in stochastic optimization and mathematical economics, Moskva, 89- 130, 1986. [2153] Christian Kredler. An SQP-method for linearly constrained maximum likelihood problems. In Applied mathematics and parallel computing, pages 157–174. Physica, Heidelberg, 1996. [2154] J. Kreimer. Generalized estimates for performance sensitivities of stochastic systems. Math. Com- put. Modelling 10, No.12, 911-922, 1988.

121 [2155] J. Kreimer and R.Y. Rubinstein. Smoothed functionals and constrained stochastic approximation. SIAM J. Numer. Anal., 25(2):470–487, 1988. [2156] Moshe Kress. The chance constrained critical path with location-scale distributions. Eur. J. Oper. Res. 18, 359-363, 1984. [2157] Ortwin Kreutzberger. Bemerkungen zur Quotienten- und Produktoptimierung mit Anwendung beim Risikoproblem der stochastischen Optimierung. Wiss. Z. Martin-Luther Univ. Halle- Wittenberg, Math.-naturw. R. 27, No.3, 75-79, 1978. [2158] Ortwin Kreutzberger and Lothar Kuegler. Bestimmung von Stabilitaetsbereichen in der stochastischen linearen Optimierung mit Hilfe parametrischer Optimierung und Regressionsrechnung. Wiss. Z., Martin-Luther-Univ. Halle-Wittenberg, Math.-Naturwiss. Reihe 26, No.5, 71-79, 1977. [2159] A. Krishnamoorthy and P. V. Ushakumari. k-out-of-n G system with repair: the D-policy. Comput. Oper. Res., 28(10):973–981, 2001. [2160] Trine Krogh Kristoffersen. Deviation measures in linear two-stage stochastic programming. Math. Methods Oper. Res., 62(2):255–274, 2005. [2161] Nikolai Krivulin. An analysis of gradient estimates in stochastic network optimization problems. In Model-oriented data analysis (Petrodvorets, 1992), Contrib. Statist., pages 227–240. Physica, Heidelberg, 1993. [2162] Nikolai Krivulin. Unbiased estimates for gradients of stochastic network performance measures. Acta Appl. Math., 33(1):21–43, 1993. Stochastic optimization. [2163] P. Krokhmal, S. Uryasev, and G. Zrazhevsky. Numerical comparison of conditional value-at-risk and conditional drawdown-at-risk approaches: application to hedge funds. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 609–631. SIAM, Philadel- phia, PA, 2005. [2164] Pavlo Krokhmal, Robert Murphey, Panos Pardalos, and Stanislav Uryasev. Use of conditional value-at-risk in stochastic programs with poorly deﬁned distributions. In Recent developments in cooperative control and optimization, volume 3 of Coop. Syst., pages 225–241. Kluwer Acad. Publ., Boston, MA, 2004. [2165] Pavlo A. Krokhmal and Robert Murphey. Modeling and implementation of risk-averse preferences in stochastic programs using risk measures. In Robust optimization-directed design, volume 81 of Nonconvex Optim. Appl., pages 95–116. Springer, New York, 2006. [2166] Piotr Krysta and Roberto Solis-Oba. Approximation algorithms for bounded facility location problems. J. Comb. Optim., 5(2):233–247, 2001. [2167] Mikio Kubo and Hiroshi Kasugai. Randomized decision strategy for the hierarchical optimization problems. J. Oper. Res. Soc. Japan 33, No.4, 335-353, 1990. [2168] Christian Kuchler¨ and Stefan Vigerske. Decomposition of multistage stochastic programs with re- combining scenraio trees. Stochastic Programming E-Print Series, http://www.speps.org, 2007. [2169] A. Kucia and A. Nowak. On -optimal continuous selectors and their application in discounted dynamic programming. J. Optimization Theory Appl. 54, 289-302, 1987. [2170] V. I.¯ Kud¯in and G. I.¯ Kud¯in. Application of the small parameter method to the investigation of weakly nonlinear systems. II. Visn.¯ Kiiv.¨ Univ.¯ Ser. Fiz.-Mat.¯ Nauki, (3):252–256, 2000. [2171] Daniel Kuhn. Aggregation and discretization in multistage stochastic programming. Stochastic Programming E-Print Series, http://www.speps.org, 2005.

122 [2172] Daniel Kuhn. Generalized bounds for convex multistage stochastic programs, volume 548 of Lec- ture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin, 2005. [2173] Daniel Kuhn. Convergent bounds for stochastic programs with expected value constraints. Stochas- tic Programming E-Print Series, http://www.speps.org, 2006. [2174] O.Yu. Kul’chitskij. Non-Markov algorithms for statistical optimization with continuous time. I. Autom. Remote Control 39, 680-691 translation from Avtom. Telemekh. 1978, No.5, 73-86 (1978)., 1978. [2175] O.Yu. Kul’chitskij. Non-Markovian algorithms for statistical optimization with continuous time. II. Autom. Remote Control 39, 823-832 translation from Avtom. Telemekh. 1978, No.6, 56-66 (1978)., 1978. [2176] O.Yu. Kul’chitskij. Sufﬁcient conditions for convergence of stochastic approximation algorithms for random processes with continuous time. Cybernetics 15, 901-917 translation from Kibernetika 1979, No.6, 114-126 (1979)., 1980. [2177] O.Yu. Kul’chitskij. Accelerated convergence effect in stochastic programming algorithms with correlated noise. Autom. Remote Control 47, 375-379 translation from Avtom. Telemekh. 1986, No.3, 94-99 (1986)., 1986. [2178] Rudolf Kulhavy.´ Recursive nonlinear estimation, volume 216 of Lecture Notes in Control and Information Sciences. Springer-Verlag London Ltd., London, 1996. A geometric approach. [2179] V.G. Kulkarni and J.S. Provan. An improved implementation of conditional Monte Carlo estimation of path lengths in stochastic networks. Oper. Res. 33, 1389-1393, 1985. [2180] Vidyadhar G. Kulkarni. Modeling and Analysis of Stochastic Systems. Texts in Statistical Science Series. Chapman and Hall Ltd., London, 1995. [2181] S. Kumar. Chance-constrained programming problem with chance-constrained relative lower bounded variables. Trabajos Estadist.´ Investigacion´ Oper., 30(2):73–77, 1979. [2182] P. L. Kunsch and J. Teghem. Nuclear-fuel cycle optimization using multiobjective stochastic linear programming. European Journal of Operational Research, 31(2):240–249, 1987. [2183] P.L. Kunsch. Application of “STRANGE” to energy studies. In Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, volume 6 of Theory Decis. Lib. Ser. D System Theory Knowledge Engrg. Probl. Solving, pages 117–130. Kluwer Acad. Publ., Dor- drecht, 1990. [2184] Alexandra Kunzi-Bay¨ and Janos´ Mayer. Computational aspects of minimizing conditional value- at-risk. Comput. Manag. Sci., 3(1):3–27, 2006. [2185] V. Yu. Kurbakovskii. A numerical method for solving an inverse probability problem. In Analysis and design of dynamical systems under conditions of uncertainty (Russian), pages 11–18. Moskov. Aviatsion. Inst., Moscow, 1990. [2186] Yasuaki Kurokawa and Kenjiro Nakamura. Forest management planning under uncertainty. J. Operations Res. Soc. Japan 20, 259-272, 1977. [2187] Harold J. Kushner. Necessary conditions for discrete parameter stochastic optimization problems. In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. III: Probability theory, pages 667–685, Berkeley, Calif., 1972. Univ. California Press. [2188] Harold J. Kushner. Stochastic approximation algorithms for constrained optimization problems. Ann. Statist., 2:713–723, 1974.

123 [2189] Harold J. Kushner. Rates of convergence for sequential Monte Carlo optimization methods. SIAM J. Control Optim., 16(1):150–168, 1978. [2190] Harold J. Kushner. Approximation methods for the minimum average cost per unit time problem with a diffusion model. In Approximate solution of random equations, pages 107–126, New York, 1979. North-Holland. [2191] Harold J. Kushner and Milton L. Kelmanson. Stochastic approximation algorithms of the multiplier type for the sequential Monte Carlo optimization of stochastic systems. SIAM J. Control Optimization, 14(5):827–842, 1976. [2192] Harold J. Kushner and Jichuan Yang. A Monte Carlo method for sensitivity analysis and parametric optimization of nonlinear stochastic systems: the ergodic case. SIAM J. Control Optim., 30(2):440– 464, 1992. [2193] H.J. Kushner and D.S. Clark. A stochastic approximation projection algorithm for constrained Monte- Carlo optimization. In A link between science and applications of automatic control, Proc. 7th trienn. World Congr., Helsinki 1978, Vol. 4, 2425-2433, 1979. [2194] V.S. Kuzin. Analytical solution of the probabilities of an optimization problem when there are rigid constraints. Soviet J. Comput. Systems Sci., 30(4):125–130, 1992. [2195] V.A. Labkovskii. Control under an independent change of the nonobservable parameter. Kiber- netika (Kiev), 2:51–57, 133, 1987. [2196] Petr Lachout. On multifunction transforms of probability measures. Ann. Oper. Res., 56:241–249, 1995. Stochastic programming (Udine, 1992). [2197] R.R. Laferriere and S.M. Robinson. Scenario analysis in u.s. army decision making. Phalanx, 33(1):10ff, 2000. [2198] Jean-Jacques Laffont. First-order certainty equivalence with instrument-dependent randomness. Review economic Studies 42, 605-614, 1975. [2199] J.C. Lagarias and F. Aminzadeh. Multi-stage planning and the extended linear-quadratic-Gaussian control problem. Math. Oper. Res. 8, 42-61, 1983. [2200] B.J. Lageweg, J.K. Lenstra, A.H.G. Rinnooy Kan, and L. Stougie. Stochastic integer programming by dynamic programming. Stat. Neerl. 39, 97-113, 1985. [2201] B.J. Lageweg, J.K. Lenstra, A.H.G. Rinnooy Kan, and L. Stougie. Stochastic integer programming by dynamic programming. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 403–412. Springer, Berlin, 1988. [2202] Constantino M. Lagoa, Xiang Li, and Mario Sznaier. Probabilistically constrained linear programs and risk-adjusted controller design. SIAM J. Optim., 15(3):938–951 (electronic), 2005. [2203] Hang-Chin Lai and Kensuke Tanaka. On continuous-time discounted stochastic dynamic programming. Appl. Math. Optim., 23(2):155–169, 1991. [2204] T.L. Lai. Stochastic approximation and sequential search for optimum. In Proceedings of the Berkeley conference in honor of Jerzy Neyman and Jack Kiefer, Vol. II (Berkeley, Calif., 1983), Wadsworth Statist./Probab. Ser., pages 557–577, Belmont, Calif., 1985. Wadsworth. [2205] Kim Fung Lam and Jane W. Moy. A simple weighting scheme for classiﬁcation in two-group discriminant problems. Comput. Oper. Res., 30(1):155–164, 2003. [2206] K. Lampe. Numerischer Vergleich des dualen und primalen Vektoroptimierungsproblemms mit dem stochastischen Suchverfahren von Timmel. Wiss. Z. Tech. Hochsch. Ilmenau 31, No.2, 93- 100, 1985.

124 [2207] M.N. Lane and S.C. Littlechild. A stochastic programming approach to weather-dependent pricing for water resources. In Stochastic programming, Proc. int. Conf., Oxford 1974, 357-368, 1980. [2208] G. Laporte, F.V. Louveaux, and L. van Hamme. Exact solution of a stochastic location problem by an integer L-shaped algorithm. Transportation Science, 28(2):95–103, 1994. [2209] Gilbert Laporte and Francois Louveaux. Formulations and bounds for the stochastic capacitated vehicle routing problem with uncertain supplies. In Economic decision-making: games, econometrics and optimisation, Contrib. in Honour of J. H. Dreze, 443-455, 1990. [2210] Gilbert Laporte, Francois Louveaux, and Helene Mercure. The vehicle routing problem with stochastic travel times. Transp. Sci. 26, No.3, 161-170, 1992. [2211] Gilbert Laporte and François V. Louveaux. The integer L-shaped method for stochastic integer programs with complete recourse. Oper. Res. Lett., 13(3):133–142, 1993. [2212] Gilbert Laporte, François V. Louveaux, and Hel´ ene` Mercure. A priori optimization of the probabilistic traveling salesman problem. Oper. Res., 42(3):543–549, 1994. [2213] Yu. P. Laptin. Construction of heuristic search strategies in the branch-and-bound method in solving the multidimensional knapsack problem. In Methods of investigation of extremal problems, pages 109–115, 124, Kiev, 1981. Akad. Nauk Ukrain. SSR Inst. Kibernet. [2214] Robert E. Larson and John L. Casti. Principles of dynamic programming. Part II: Advanced theory and applications. Control and Systems Theory, Vol. 7. New York and Basel: Marcel Dekker, Inc., 1982. [2215] J.B. Lasserre. Exact formula for sensitivity analysis of Markov chains. J. Optim. Theory Appl., 71(2):407–413, 1991. [2216] J.B. Lasserre, C. Bes, and F. Roubellat. The stochastic discrete dynamic lot size problem: an open-loop solution. Operations Research, 33(3):684–689, 1985. [2217] Jean B. Lasserre. Duality and randomization in nonlinear programming. ANZIAM J., 42((E)):E27– E68, 2000/01. [2218] Zoltan Laszlo. Ueber wahrscheinlichkeitsbeschraenkte Lagerhaltungsmodelle. Magyar Tud. Akad. mat. fiz. Tud. Oszt. Koezl. 21 77-117 (1973)., 1972. [2219] Karen K. Lau and Robert S. Womersley. Multistage quadratic stochastic programming. J. Com- put. Appl. Math., 129(1-2):105–138, 2001. Nonlinear programming and variational inequalities (Kowloon, 1998). [2220] T. W. Edward Lau and Y. C. Ho. Universal alignment probabilities and subset selection for ordinal optimization. J. Optim. Theory Appl., 93(3):455–489, 1997. [2221] Purushottam W. Laud, L. Mark Berliner, and Prem K. Goel. A stochastic probing algorithm for global optimization. J. Global Optim., 2(2):209–224, 1992. [2222] Jean-Louis Lauriere. Elements de programmation dynamique. Preface de Robert Faure. Recherche Operationnelle Appliquee, 3. Collection ”Programmation”. Paris: Gauthier-Villars., 1979. [2223] Irving H. LaValle. On information-augmented chance-constrained programs. Oper. Res. Lett., 4(5):225–230, 1986. [2224] Irving H. Lavalle. On the “Bayesability” of chance-constrained programming problems. Oper. Res. Lett., 4(6):281–283, 1986. [2225] Irving H. Lavalle. On the Bayesability of chance-constrained programs: a clarification. Oper. Res. Lett., 5(5):261, 1986.

125 [2226] Irving H. Lavalle. Response to: “Use of sample information in stochastic recourse and chance- constrained programming models” [Management Sci. 31 (1985), no. 1, 96–108; MR 87e:90074] by R. Jagannathan: on the “Bayesability” of CCPs. Management Sci., 33(10):1224–1231, 1987. With a reply by Jagannathan. [2227] E.¯ P. Lavrinenko. A certain stochastic programming problem. In Cybernetics and computer technology, No. 8: Complex control systems (Russian), pages 68–71, Kiev, 1971. “Naukova Dumka”. [2228] E.¯ P. Lavrinenko. Pareto-optimal solutions in problems of vector stochastic optimization. In Ques- tions in the study of multicriteria optimization problems, volume 22 of Preprint 81, pages 40–51, 55. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1981. [2229] E.P. Lavrinenko. Ueber ein Problem der Programmsteuerung im hierarchischen Zweiniveausystem unter Unbestimmtheitsverhaeltnissen. In Kibernetika vycislit. Tehn. 19, slozn. Sist. Upravl., 9-13, 1973. [2230] J.P. Lawrence III and Kenneth Steiglitz. Randomized pattern search. IEEE Trans. Comput. C- 21, 382-385, 1972. [2231] Andrew J. Lazarus. Certain expected values in the random assignment problem. Oper. Res. Lett., 14(4):207–214, 1993. [2232] Jean-Sebastien´ Le Brizaut. Une methode´ d’optimisation stochastique pour evaluer´ des minima a` pres.` Bull. Sci. Math., 126(8):693–703, 2002. [2233] Larry J. LeBlanc. Optimization models for distribution planning. In Risk and capital (Ulm, 1983), volume 227 of Lecture Notes in Econom. and Math. Systems, pages 203–223. Springer, Berlin, 1984. [2234] J.P. Leclercq. La programmation lineaire´ stochastique: une approche multicritere.` I. Formulation. Cahiers Centre Etudes´ Rech. Oper.´ , 23(1):31–41, 1981. [2235] J.P. Leclercq. La programmation lineaire´ stochastique: une approche multicritere.` II. Un algorithme interactif adapte´ aux distributions multinormales. Cahiers Centre Etudes´ Rech. Oper.´ , 23(2):121– 132, 1981. [2236] J.P. Leclercq. Stochastic programming: an interactive multicriteria approach. European J. Oper. Res., 10(1):33–41, 1982. [2237] Pierre L’Ecuyer and Alain Haurie. Preventive replacement for multicomponent systems: An op- portunistic discrete-time dynamic programming model. IEEE Trans. Reliab. R-32, 117-118, 1983. [2238] Pierre L’Ecuyer and Gaetan´ Perron. On the convergence rates of IPA and FDC derivative estimators. Oper. Res., 42(4):643–656, 1994. [2239] Sang M. Lee and David L. Olson. A gradient algorithm for chance constrained nonlinear goal programming. Eur. J. Oper. Res. 22, 359-369, 1985. [2240] Peter P. Lehleiter. Optimale Steuerung der Bedienung exponentieller Wartesysteme mit vorgegebener Kundenzahl. (Optimal service control for exponential queueing systems with pre- determined number of customers)., 1984. [2241] Guiyuan Lei. Adaptive quasi-Monte Carlo method for multiple-extrema optimization. Control Theory Appl., 19(3):431–434, 2002. [2242] Zhongxue Lei and Xianyu Li. Several convexity statements in chance constrained programming. J. Jiangxi Norm. Univ., Nat. Sci. Ed. 13, No.2, 13-19, 1989. [2243] Timo Leipal¨ a.¨ On the solutions of stochastic traveling salesman problems. European J. Oper. Res., 2(4):291–297, 1978.

126 [2244] Bernard Lemaire. About the convergence of the proximal method. In Advances in optimization (Lambrecht, 1991), volume 382 of Lecture Notes in Econom. and Math. Systems, pages 39–51. Springer, Berlin, 1992. [2245] B.J. Lence and A. Ruszczynski. Managing water quality under uncertainty: Application of a new stochastic branch and bound method. IIASA Working Paper WP-96-066, Laxenburg, Austria, 1996. [2246] J.K. Lenstra. Corrigendum: “Stochastic integer programming by dynamic programming” [Statist. Neerlandica 39 (1985), no. 2, 97–113; MR 86j:90154] by B. J. Lageweg, Lenstra, A. H. G. Rinnooy Kan and L. Stougie. Statist. Neerlandica, 40(2):129, 1986. [2247] J.K. Lenstra, A.H.G. Rinnooy Kan, and L. Stougie. A framework for the probabilistic analysis of hierarchical planning systems. In Stochastics and optimization, Sel. Pap. ISSO Meet., Gorguano/Italy 1982, Ann. Oper. Res. 1, 23-42, 1984. [2248] Cornelius T. Leondes and Ranjit K. Nandi. Capacity expansion in convex cost networks with uncertain demand. Operations Res., 23(6):1172–1178, 1975. [2249] S.L. Leonov. A stochastic algorithm for the minimization of an additive function. Avtomat. i Telemekh., 10:63–70, 1985. [2250] Cristina M.A. Leopoldino, Mario´ V.F. Pereira, Leontina M.V. Pinto, and Celso C. Ribeiro. A constraint generation scheme to probabilistic linear problems with an application to power system expansion planning. Ann. Oper. Res., 50:367–385, 1994. Applications of combinatorial optimization. [2251] R. Lepp. A projective stochastic approximation method for finding an admissible point in stochastic programming. Eesti NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 26(2):128–134, 1977. [2252] R. Lepp. Deterministic equivalents of stochastic programming problems with elliptically symmetric distributions. Eesti NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 28(2):158–160, 180, 1979. [2253] R. Lepp. Maximization of a probability function on simple sets. Eesti NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 28(4):303–309, 1979. [2254] R. Lepp. Minimization of a smooth function under probabilistic constraints. Eesti NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 29(2):140–144, 229, 1980. [2255] R. Lepp. Stochastic approximation type algorithm for the maximization of the probability function. Izv. Akad. Nauk Ehst. SSR, Fiz., Mat. 32, 150-156, 1983. [2256] R. Lepp. Conditions for discrete stability of the general stochastic programming problem with decision functions. Eesti NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 35(1):20–27, 122, 1986. [2257] R. Lepp. Discrete stability of stochastic programming problems with recourse. In System modelling and optimization, Proc. 12th IFIP Conf., Budapest/Hung. 1985, Lect. Notes Control Inf. Sci. 84, 529-534, 1986. [2258] R. Lepp. On the approximation of stochastic convex programming problems. In Stochastic optimization (Kiev, 1984), volume 81 of Lecture Notes in Control and Inform. Sci., pages 427–434. Springer, Berlin, 1986. [2259] R. Lepp. Discrete approximation of linear two-stage stochastic programming problem. Numer. Funct. Anal. Optim., 9(1-2):19–33, 1987. [2260] R. Lepp and V. Ol’man. An inequality for integrals with spherically symmetric functions and its application to optimization. Eesti NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 29(2):133–139, 229, 1980.

127 [2261] R. Lepp and E. Raik. Randomized solutions in stochastic programming problems. Eesti NSV Tead. Akad. Toimetised Fu¨us.-Mat.¨ , 21:379–386, 1972. [2262] R. E.` Lepp. Approximation of a problem of operative stochastic programming. Issled. Operatsii i ASU, 26:20–26, 117, 1985. [2263] R. E.` Lepp. Approximation of the probability functional. In Analysis of stochastic systems by methods in operations research and reliability theory (Russian), pages 17–21, ii, Kiev, 1987. Akad. Nauk Ukrain. SSR Inst. Kibernet. [2264] R. E.` Lepp. Approximation of a problem of stochastic programming with complete recursion. Dokl. Akad. Nauk SSSR, 305(6):1307–1310, 1989. [2265] R.E. Lepp. Investigations of Estonian scientists on stochastic programming. Izv. Akad. Nauk SSSR, Tekh. Kibern. 1982, No.6, 57-64, 1982. [2266] R.E. Lepp. Investigations of Estonian scientists on stochastic programming. Engrg. Cybernetics, 20(6):11 (1983), 1982. [2267] R.E.` Lepp. Discrete approximation and stability of a stochastic programming problem with complete recursion. Zh. Vychisl. Mat. i Mat. Fiz., 27(7):993–1004, 1117, 1987. [2268] R.E. Lepp. Approximation of decision rules in stochastic programming. J. Comput. Systems Sci. Internat., 31(2):46–49, 1993. [2269] Riho Lepp. Approximate solution of stochastic programming problems with recourse. Kybernetika (Prague), 23(6):476–482, 1987. [2270] Riho Lepp. Approximations to stochastic programs with complete recourse. SIAM J. Control Optim., 28(2):382–394, 1990. [2271] Riho Lepp. Discrete approximation of extremum problems with operator constraints. In System modelling and optimization (Leipzig, 1989), volume 143 of Lecture Notes in Control and Inform. Sci., pages 170–176. Springer, Berlin, 1990. [2272] Riho Lepp. Projection and discretization methods in stochastic programming. J. Comput. Appl. Math., 56(1-2):55–64, 1994. Stochastic programming: stability, numerical methods and applications (Gosen, 1992). [2273] Riho Lepp. Approximation of extremum problems with probability cost functionals. In Stochas- tic programming methods and technical applications (Neubiberg/Munich, 1996), pages 169–185. Springer, Berlin, 1998. [2274] Riho Lepp. Approximation of the quantile minimization problem with decision rules. Optim. Methods Softw., 17(3):505–522, 2002. Stochastic programming. [2275] Riho Lepp. Discrete approximation of extremum problems with chance constraints. In Stochastic optimization techniques (Neubiberg/Munich, 2000), volume 513 of Lecture Notes in Econom. and Math. Systems, pages 21–33. Springer, Berlin, 2002. [2276] L.L. Leshchenko. On a stochastic transportation problem. Issled. Oper. ASU 23, 43-50, 1984. [2277] Reuven R. Levary. An experimental sequential solution procedure to stochastic linear programming problems with 0 − 1 variables. Internat. J. Systems Sci., 15(10):1073–1085, 1984. [2278] V.L. Levin. Extremal problems with probability measures, functionally closed preorders and strong stochastic dominance. In Stochastic optimization, Proc. Int. Conf., Kiev/USSR 1984, Lect. Notes Control Inf. Sci. 81, 435-447, 1986.

128 [2279] Art Lew. Nondeterministic dynamic programming on a parallel coprocessing system. Appl. Math. Comput., 120(1-3):139–147, 2001. The Bellman continuum (Santa Fe, NM, 1999). [2280] D. Li, X. L. Sun, M. P. Biswal, and F. Gao. Convexification, concavification and monotonization in global optimization. Ann. Oper. Res., 105:213–226 (2002), 2001. Geometric programming. [2281] Donghui Li. Two methods for undiscounted Markov decision programming. Hunan Ann. Math. 7, No.2, 97-103, 1987. [2282] Duan Li. Multiple objectives and nonseparability in stochastic dynamic programming. Internat. J. Systems Sci., 21(5):933–950, 1990. [2283] Duan Li and Yacov Y. Haimes. The uncertainty sensitivity index method (USIM) and its extension. Nav. Res. Logist. 35, No.6, 655-672, 1988. [2284] Hua Li and Xing Si Li. Solutions of minimum cross-entropy optimization problems with cross- entropy constraints. J. Lanzhou Univ. Technol., 32(1):148–151, 2006. [2285] Wu-Ji Li and J. MacGregor Smith. Stochastic quadratic assignment problems. In Quadratic assignment and related problems (New Brunswick, NJ, 1993), volume 16 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., pages 221–236. Amer. Math. Soc., Providence, RI, 1994. [2286] Xiao Li Li and Gong Yan Lei. Some comments about stochastic optimization algorithms. Math. Numer. Sinica, 18(4):435–441, 1996. [2287] Xiao Li Li and Jian Hui Ren. Stability of optimal values and optimal solution sets of stochastic programming. J. Shaanxi Normal Univ. Nat. Sci. Ed., 32(4):27–30, 2004. [2288] Xiao Liu Li and Jin De Wang. Approximate feasible direction method for stochastic programming problems with recourse. Linear inequality deterministic constraints. Optimization, 21(3):401–407, 1990. [2289] X.S. Li and A.B. Templeman. An informational entropy approach to optimization. In Approxima- tion, optimization and computing, pages 263–266. North-Holland, Amsterdam, 1990. [2290] Y. Li and D. Wang. A semi-infinite programming model for earliness/tardiness production planning with simulated annealing. Math. Comput. Modelling, 26(7):35–42, 1997. [2291] Y. P. Li, G. H. Huang, S. L. Nie, X. H. Nie, and I. Maqsood. An interval-parameter two-stage stochastic integer programming model for environmental systems planning under uncertainty. Eng. Optim., 38(4):461–483, 2006. [2292] Marek Libura. Integer programming problems with inexact objective function. Control Cybern. 9, 189-202, 1980. [2293] Bennet P. Lientz. Stochastic allocation of spare components. In Optimizing Meth. Statist., Proc. Sympos. Ohio State Univ. 1971, 403-412 , 1971. [2294] V.E. Lihtenstein. Diskretheit und Zufaelligkeit in oekonomisch-mathematischen Problemen. (Diskretnost’ i slucainost’ v ekonomiko-matematiceskih zadacah.). Moskau: Verlag ’Nauka’., 1973. [2295] Gui-Hua Lin and Masao Fukushima. A class of stochastic mathematical programs with complementarity constraints: reformulations and algorithms. J. Ind. Manag. Optim., 1(1):99–122, 2005. [2296] Gui-Hua Lin and Masao Fukushima. Regularization method for stochastic mathematical programs with complementarity constraints. ESAIM Control Optim. Calc. Var., 11(2):252–265 (electronic), 2005.

129 [2297] Gui-Hua Lin and Masao Fukushima. New reformulations for stochastic nonlinear complementarity problems. Optim. Methods Softw., 21(4):551–564, 2006. [2298] Jianhua Lin and S.K.M. Wong. Approximation of discrete probability distributions based on a new divergence measure. Congr. Numer., 61:75–80, 1988. Seventeenth Manitoba Conference on Numerical Mathematics and Computing (Winnipeg, MB, 1987). [2299] S. Y. Lin and Y. C. Ho. Universal alignment probability revisited. J. Optim. Theory Appl., 113(2):399–407, 2002. [2300] Xiaocang Lin and Loo Hay Lee. A new approach to discrete stochastic optimization problems. European J. Oper. Res., 172(3):761–782, 2006. [2301] Zhenghua Lin and Weisheng Yu. The twice continuously differentiable property of two-stage stochastic linear programming problems with fixed recourse. Soochow J. Math., 23(2):157–164, 1997. [2302] Jeff Linderoth, Alexander Shapiro, and Stephen Wright. The empirical behavior of sampling methods for stochastic programming. Ann. Oper. Res., 142:215–241, 2006. [2303] Jeff Linderoth and Stephen Wright. Decomposition algorithms for stochastic programming on a computational grid. Stochastic Programming E-Print Series, http://www.speps.org, 2001. [2304] Jeff Linderoth and Stephen Wright. Decomposition algorithms for stochastic programming on a computational grid. Optimization Online, http://www.optimization-online.org, 2001. [2305] Jeff Linderoth and Stephen J. Wright. Computational grids for stochastic programming. In Ap- plications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 61–77. SIAM, Philadelphia, PA, 2005. [2306] Chen Ling, Xiaojun Chen, Masao Fukushima, and Liqun Qi. A smoothing implicit programming approach for solving a class of stochastic generalized semi-infinite programming problems. Pac. J. Optim., 1(1):127–145, 2005. [2307] B.P. Lingaraj. Certainty equivalent of a chance constraint if the random variable is uniformly distributed. Comm. Statist., 3(10):949–951, 1974. [2308] B.P. Lingaraj and Harvey Wolfe. Certainty equivalent of a chance constraint if the random variable follows a gamma distribution. Sankhya¯ Ser. B, 36(2):204–208, 1974. [2309] K. Linowsky and A. B. Philpott. On the convergence of sampling-based decomposition algorithms for multistage stochastic programs. J. Optim. Theory Appl., 125(2):349–366, 2005. [2310] Svante Linusson and Johan Wastlund.¨ A proof of Parisi’s conjecture on the random assignment problem. Probab. Theory Related Fields, 128(3):419–440, 2004. [2311] Joseph Lipscomb and David Zalkind. Deterministic models for production of services with stochastic technology. Econometrica, 48(5):1169–1186, 1980. [2312] Baoding Liu. Dependent-chance goal programming and its genetic algorithm based approach. Math. Comput. Modelling, 24(7):43–52, 1996. [2313] Baoding Liu. Dependent-chance programming: a class of stochastic optimization. Comput. Math. Appl., 34(12):89–104, 1997. [2314] Chih-Ming Liu and Jerry L. Sanders. Stochastic design optimization of asynchronous flexible assembly systems. Ann. Oper. Res. 15, 131-154, 1988.

130 [2315] Chuan Cai Liu. Convergence rate of moments for stochastic perturbation gradient approximation. J. Fuzhou Univ. Nat. Sci. Ed., 30(1):28–32, 2002. [2316] M.L. Liu and N.V. Sahinidis. Optimization in process planning under uncertainty. Industrial & Engineering Chemistry Research, 35(11):4154-4165, 1996. [2317] P.T. Liu and J.G. Sutinen. Pareto optimal leasing and investment policies for a publicly owned exhaustible resource. In New trends in dynamic system theory and economics, Proc. Semin., Udine/Italy 1977, 137-149, 1979. [2318] W. Liu and Y. H. Dai. Minimization algorithms based on supervisor and searcher cooperation. J. Optim. Theory Appl., 111(2):359–379, 2001. [2319] X. W. Liu and M. Fukushima. Parallelizable preprocessing method for multistage stochastic programming problems. J. Optim. Theory Appl., 131(3):327–346, 2006. [2320] Xian Liu. Several filled functions with mitigators. Appl. Math. Comput., 133(2-3):375–387, 2002. [2321] Xian Liu. The role of stochastic programming in communication network design. Comput. Oper. Res., 32(9):2329–2349, 2005. [2322] Xinwei Liu and Jie Sun. A new decomposition technique in solving multistage stochastic linear programs by infeasible interior point methods. J. Global Optim., 28(2):197–215, 2004. [2323] Yian-Kui Liu and Baoding Liu. Random fuzzy programming with chance measures defined by fuzzy integrals. Math. Comput. Modelling, 36(4-5):509–524, 2002. [2324] John R. Liukkonen and Arnold Levine. On convergence of iterated random maps. SIAM J. Control Optim., 32(6):1752–1762, 1994. [2325] Liwan Liyanage and J. George Shanthikumar. Allocation through stochastic Schur convexity and stochastic transposition increasingness. In Stochastic inequalities (Seattle, WA, 1991), volume 22 of IMS Lecture Notes Monograph Ser., pages 253–273. Inst. Math. Statist., Hayward, CA, 1992. [2326] S.I. Ljaskoˇ and F. Mirzoahmedov. Method of feasible directions in the minimization of almost differentiable functions with unknown parameters. Akad. Nauk Ukrain. SSR Inst. Kibernet. Preprint, 13:14–20, 53, 1979. Stochastic optimization models. [2327] L. Ljung. Some basic ideas in recursive identification. In Analysis and optimisation of stochastic systems, Proc. int. Conf., Oxford 1978, 408-418, 1980. [2328] Lennart Ljung. Recursive identification. In Stochastic systems: the mathematics of filtering and identification and applications, Proc. NATO Adv. Study Inst., Les Arcs/Savoie/ France 1980, 247- 281, 1981. [2329] C. Lobry. Une propriete de l’ensemble des etats accessibles d’un systeme guidable. C. R. Acad. Sci., Paris, Ser. A 272, 153-156, 1971. [2330] M. Locatelli. Bayesian algorithms for one-dimensional global optimization. J. Global Optim., 10(1):57–76, 1997. [2331] M. Locatelli and F. Schoen. Simple linkage: analysis of a threshold-accepting global optimization method. J. Global Optim., 9(1):95–111, 1996. [2332] Marco Locatelli and Fabio Schoen. An adaptive stochastic global optimization algorithm for one- dimensional functions. Ann. Oper. Res., 58:263–278, 1995. Applied mathematical programming and modeling, II (APMOD 93) (Budapest, 1993). [2333] Marco Locatelli and Fabio Schoen. Theoretical and experimental analysis of random linkage algorithms for global optimization. In System modelling and optimization (Prague, 1995), pages 473–480. Chapman & Hall, London, 1996.

131 [2334] Marco Locatelli and Fabio Schoen. Random Linkage: a family of acceptance/rejection algorithms for global optimisation. Math. Program., 85(2, Ser. A):379–396, 1999. [2335] A.G. Lockett and A.P. Muhlemann. A stochastic programming model for aggregate production planning. Eur. J. Oper. Res. 2, 350-356, 1978. [2336] A.G. Lockett, A.P. Muhlemann, and L.A. Wolsey. A stochastic programming model for project selection. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 427–448. Academic Press, London, 1980. [2337] A. Løkketangen and D.L. Woodruff. Progressive hedging and tabu search applied to mixed integer (0,1) multi-stage stochastic programming. Journal of Heuristics, 2:111–128, 1996. [2338] K. Lommatzsch (ed.). Programmpakete der Operationsforschung. Seminarber., Humboldt-Univ. Berlin, Sekt. Math. 22, 160 P., 1979. [2339] Domingo Lopez-Rodr´ íguez, Enrique Merida-Casermeiro,´ and J. M. Ortiz-de Lazcano-Lobato. Stochastic multivalued network for optimization: application to the graph maxcut problem. WSEAS Trans. Math., 6(3):500–505, 2007. [2340] Victor Loskutov. Models, algorithms and software of stochastic optimization. In Computational aspects of model choice (Prague, 1991), Contrib. Statist., pages 177–186. Physica, Heidelberg, 1993. [2341] D. P. Loucks. Computer models for reservoir regulation. Journal of the Sanitary Engineering Division, Proceedings of the American Society of Civil Engineers, 94(SA4):657–669, August 1968. [2342] Daniel P. Loucks. Discrete chance constrained models for river basin planning. In Stochastic programming, Proc. int. Conf., Oxford 1974, 329-340, 1980. [2343] F. Louveaux. Optimal scheduling of income tax prepayments under stochastic incomes. Eur. J. Oper. Res. 9, 26-32, 1982. [2344] Francois Louveaux and Jacques-Francois Thisse. Production and location on a network under demand uncertainty. Oper. Res. Lett. 4, 145-149, 1985. [2345] Francois V. Louveaux. Piecewise convex programs. Math. Programming 15, 53-62, 1978. [2346] François V. Louveaux. A solution method for multistage stochastic programs with recourse with application to an energy investment problem. Oper. Res., 28(4):889–902, 1980. [2347] François V. Louveaux. Multistage stochastic programs with block-separable recourse. Math. Pro- gramming Stud., 28:48–62, 1986. Stochastic programming 84. II. [2348] François V. Louveaux and D. Peeters. A dual-based procedure for stochastic facility location. Oper. Res., 40(3):564–573, 1992. [2349] François V. Louveaux and Maarten H. van der Vlerk. Stochastic programming with simple integer recourse. Math. Programming, 61(3, Ser. A):301–325, 1993. [2350] F.V. Louveaux. Discrete stochastic location models. Annals of Operations Research, 6(4):23–34, 1986. [2351] F.V. Louveaux. Stochastic programs with simple integer recourse. Manuscript, Facultes´ Universi- taires Notre-Dame de la Paix, Namur, 1991. [2352] F.V. Louveaux and Y. Smeers. Optimal investments for electricity generation: A stochastic model and a test-problem. In Numerical techniques for stochastic optimization, Springer Ser. Comput. Math. 10, 445-453, 1988.

132 [2353] William S. Lovejoy. Policy bounds for Markov decision processes. Oper. Res. 34, 630-637, 1986. [2354] David Lowell Lovelady. Iterative maximization subject to stochastic constraints. J. Math. Anal. Appl. 64, 142-145, 1978. [2355] Dinh The’ Lu’c. Duality in programming under probabilistic constraints with a random technology matrix. Probl. Control Inf. Theory 12, 429-437, 1983. [2356] R. Lucchetti and R.J-B. Wets. Convergence of minima of integral functionals with applications to optimal control and stochastic optimization. Statistics and Decisions, 11, 1993. [2357] James Luedtke and Shabbir Ahmed. A sample approximation approach for optimization with probabilistic constraints. Optimization Online, http://www.optimization-online.org, 2007. [2358] James Luedtke, Shabbir Ahmed, and George Nemhauser. An integer programming approach for linear programs with probabilistic constraints. Optimization Online, http://www. optimization-online.org, 2007. [2359] M.K. Luhandjula. Flou et aleatoire en programmation lineaire. BUSEFAL 11, 33-38, 1982. [2360] M.K. Luhandjula. Programmation lineaire avec des donnees possibilistes. BUSEFAL 15, 134-143, 1983. [2361] M.K. Luhandjula. Satisfying solutions for a possibilistic linear program. Inf. Sci. 40, 247-265, 1986. [2362] M.K. Luhandjula. Linear programming with a possibilistic objective function. Eur. J. Oper. Res. 31, 110-117, 1987. [2363] M.K. Luhandjula. Multiple objective programming problems with possibilistic coefﬁcients. Fuzzy Sets Syst. 21, 135-145, 1987. [2364] M.K. Luhandjula and M.M. Gupta. On fuzzy stochastic optimization. Fuzzy Sets and Systems, 81(1):47–55, 1996. Fuzzy optimization. [2365] Monga Kalonda Luhandjula. Linear programming under randomness and fuzziness. Fuzzy Sets Syst. 10, 45-55, 1983. [2366] S. Lukasik. Optimale Steuerung in hierarchischen mehrkriteriellen Systemen unter den Bedin- gungen unvollstandiger¨ Information. In Polyoptimization—theoretic foundations and applications (Sem., Bad Stuer, 1976) (German), volume 2 of ZKI-Inform. 78, pages 87–103. Akad. Wiss. DDR, Berlin, 1978. [2367] Guglielmo Lulli and Suvrajeet Sen. A branch-and-price algorithm for multi-stage stochastic integer programming with application to stochastic batch-sizing problems. Stochastic Programming E- Print Series, http://www.speps.org, 2002. [2368] Guglielmo Lulli and Suvrajeet Sen. A heuristic procedure for stochastic integer programs with complete recourse. European J. Oper. Res., 171(3):879–890, 2006. [2369] R.R. Luman. Quantitative decision support for upgrading complex systems of systems. Ph.D. thesis, School of Engineering and Applied Science, George Washington University, 1997. [2370] R.R. Luman. Upgrading complex systems of systems: a CAIV methodology for warfare area requirements analysis. Military Operations Research, 52:53–75, 2000. [2371] Morten W. Lund. Valuing ﬂexibility in offshore petroleum projects. Ann. Oper. Res., 99:325–349 (2001), 2000. Applied mathematical programming and modeling, IV (Limassol, 1998).

133 [2372] M. Lundy and A. Mees. Convergence of an annealing algorithm. Math. Programming, 34(1):111– 124, 1986. [2373] Chengjie Luo, Clement Yu, Jorge Lobo, Gaoming Wang, and Tracy Pham. Computation of best bounds of probabilities from uncertain data. Comput. Intelligence, 12(4):541–566, 1996. [2374] Jian Wen Luo and Shi Jie Lu. Convergence of approximate solutions in stochastic programming. J. Zhejiang Univ. Sci. Ed., 27(5):493–497, 2000. [2375] Jian Wen Luo and Shi Jie Lu. Stability analysis for probabilistic constrained programs. Appl. Math. J. Chinese Univ. Ser. A, 16(1):119–124, 2001. [2376] Jian Wen Luo and Jin De Wang. Weak differentiability in stochastic programming. Gaoxiao Yingyong Shuxue Xuebao Ser. A, 12(1):53–62, 1997. [2377] Irvin J. Lustig, John M. Mulvey, and Tamra J. Carpenter. Formulating two-stage stochastic programs for interior point methods. Oper. Res., 39(5):757–770, 1991. [2378] S.I. Lyashko and F. Mirzoakhmedov. Some methods of joint identification and optimization. Dokl. Akad. Nauk Tadzh. SSR 24, 721-727, 1981. [2379] S.I. Lyashko and F. Mirzoakhmedov. Some methods of simultaneous identification and optimization. Dokl. Akad. Nauk Tadzhik. SSR, 24(12):721–724, 1981. [2380] Norman R. Lyons. Resource planning for randomly arriving stochastic jobs. Management Sci., Appl. 21, 931-936, 1975. [2381] G. I. Lyubchenko and A. N. Nakonechnyi. Optimization methods for compound Poisson risk processes. Kibernet. Sistem. Anal., (2):87–96, 188, 1998. [2382] A. Maatman, C. Schweigman, A. Ruijs, and M.H. van der Vlerk. Modeling farmers’ response to uncertain rainfall in burkina faso: a stochastic programming approach. Operations Research, 50(3):399–414, 2002. [2383] Odile Macchi and Eweda Eweda. Second-order convergence analysis of stochastic adaptive linear filtering. IEEE Trans. Autom. Control AC-28, 76-85, 1983. [2384] M. E. P. Maceira and J. M. Damazio.´ Use of the PAR(p) model in the stochastic dual dynamic programming optimization scheme used in the operation planning of the Brazilian hydropower system. Probab. Engrg. Inform. Sci., 20(1):143–156, 2006. [2385] R.Infante Macias. Bemerkung ueber lineare stochastische Programmierung: Entwicklung und ak- tueller Stand. I. Trabajos Estadist. Investig. operat. 23, No.1/2, 9-49, 1972. [2386] L.C. MacLean. Lagrange multipliers in chance constrained programming. Methods Oper. Res. 41, 165-167, 1981. [2387] Leonard MacLean, Rafael Sanegre, Yonggan Zhao, and William T. Ziemba. Capital growth with security. Stochastic Programming E-Print Series, http://www.speps.org, 2002. [2388] Leonard C. MacLean and William T. Ziemba. Growth versus security tradeoffs in dynamic investment analysis. Ann. Oper. Res., 85:193–225, 1999. Stochastic programming. State of the art, 1998 (Vancouver, BC). [2389] Leonard C. MacLean, William T. Ziemba, and Yuming Li. Time to wealth goals in capital accumulation. Stochastic Programming E-Print Series, http://www.speps.org, 2000. [2390] Marilyn J. Maddox and John R. Birge. Using second moment information in stochastic scheduling. In Recent advances in control and optimization of manufacturing systems, volume 214 of Lecture Notes in Control and Inform. Sci., pages 99–120. Springer, London, 1996.

134 [2391] G. Madi-Nagy.´ A method to ﬁnd the best bounds in a multivariate discrete moment problem if the basis structure is given. Studia Sci. Math. Hungar., 42(2):207–226, 2005. [2392] Y. Maeda. Time difference simultaneous perturbation method. Electronics Letters, 32:1016–1018, 1996. [2393] Y. Maeda and R.J.P. De Figueiredo. Learning rules for neuro-controller via simultaneous perturbation. IEEE Transactions on Neural Networks, 8:1119–1130, 1997. [2394] Y. Maeda, H. Hirano, and Y. Kanata. A learning rule of neural networks via simultaneous perturbation and its hardware implementation. Neural Networks, 8:251–259, 1995. [2395] Y. Maeda, A. Nakazawa, and K. Yakichi. Hardware implementation of a pulse density neural network using simultaneous perturbation learning rule. Analog Intergrated Circuits and Signal Processing, 18:153–162, 1999. [2396] P.M. Maekilae. A self-tuning regulator based on optimal output feedback theory. Automatica 20, 671-679, 1984. [2397] F. Mafﬁoli, M.G. Speranza, and C. Vercellis. Randomized algorithms: An annotated bibliography. In Stochastics and optimization, Sel. Pap. ISSO Meet., Gorguano/Italy 1982, Ann. Oper. Res. 1, 331-345, 1984. [2398] P. Maillard. Contribution a` l’etude´ des problemes` de transport. Publ. Econom´ etriques´ , 10(1):19–41, 87, 1977. [2399] A.A.K. Majumdar. On a generalized secretary problem with three stops under a linear travel cost. Indian J. Math., 33(2):189–202, 1991. [2400] A.A.K. Majumdar. A best-choice problem with three stops and random termination. Sankhya¯ Ser. B, 57(1):76–84, 1995. [2401] Mukul Majumdar. A note on learning and optimal decisions with a partially observable state space. In Essays in the economics of renewable resources, Contrib. econ. Anal. 143, 141-153, 1982. [2402] Mukul Majumdar and Tapan Mitra. Robust ergodic chaos in discounted dynamic optimization models. Econom. Theory, 4(5):677–688, 1994. [2403] Mukul Majumdar and Itzhak Zilcha. Optimal growth in a stochastic environment: Some sensitivity and turnpike results. J. Econ. Theory 43, 116-133, 1987. [2404] W.K. Mak, D.P. Morton, and R.K. Wood. Monte carlo bounding techniques for determining solution quality in stochastic programs. Operations Research Letters, 24:47–56, 1999. [2405] Algirdas Makauskas. On a possibility to use gradients in statistical models of global optimization of objective functions. Informatica, 2(2):248–254, 316, 324, 1991. [2406] Yu.I. Maksimov. Stochastic simultion in planning. (Stokhasticheskoe modelirovanie v planirovanii). Akademiya Nauk SSSR, Sibirskoe Otdelenie. Institut Ehkonomiki i Organizatsii Promyshlennogo Proizvodstva. Novosibirsk: Izdatel’stvo ”Nauka”, Sibirskoe Otdelenie., 1981. [2407] Scott A. Malcolm and Stavros A. Zenios. Robust optimization for power systems capacity expansion under uncertainty. J. Oper. Res. Soc. 45, No.9, 1040-1049, 1994. [2408] Wilfredo L. Maldonado and B. F. Svaiter. Holder¨ continuity of the policy function approximation in the value function approximation. J. Math. Econom., 43(5):629–639, 2007. [2409] Lilia Maliar and Serguei Maliar. Solving nonlinear dynamic stochastic models: an algorithm computing value function by simulations. Econom. Lett., 87(1):135–140, 2005.

135 [2410] W. Maly and S.W. Director. Dimension reduction procedure for the simplicial approximation approach to design centering. Proc. IEE-G, 127(6):255–259, 1980. [2411] V.V. Malyshev, A.I. Kibzun, and D. E.` Chernov. Two approaches to the solution of probabilistic optimization problems. Soviet J. Automat. Inform. Sci., 20(3):20–25 (1988), 1987. [2412] John W. Mamer and Kenneth E. Schilling. On the growth of random knapsacks. Discrete Appl. Math. 28, No.3, 223-230, 1990. [2413] A. S. Manne and T. R. Olsen. Greenhouse gas abatement—toward Pareto-optimal decisions under uncertainty. Annals of Operations Research, 68:267–279, 1996. [2414] Alexander Manz¨ and Silvia Vogel. On stability of multistage stochastic decision problems. In Recent advances in optimization, volume 563 of Lecture Notes in Econom. and Math. Systems, pages 103–118. Springer, Berlin, 2006. [2415] Imran Maqsood, Guo H. Huang, and Julian Scott Yeomans. An interval-parameter fuzzy two-stage stochastic program for water resources management under uncertainty. European J. Oper. Res., 167(1):208–225, 2005. [2416] A. Marchetti Spaccamela, A.H.G. Rinnooy Kan, and L. Stougie. Hierarchical vehicle routing problems. Networks 14, 571-586, 1984. [2417] A. Marchetti-Spaccamela and C. Vercellis. Stochastic on-line knapsack problems. Math. Program- ming, 68(1, Ser. A):73–104, 1995. [2418] T.A. Marinchenko. Application of stochastic quasigradient methods for dynamical systems. In Analysis of stochastic systems by methods in operations research and reliability theory (Russian), pages 32–34, iii. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1987. [2419] Andreas Markert¨ and Rudiger¨ Schultz. On deviation measures in stochastic integer programming. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [2420] Andreas Markert¨ and Rudiger¨ Schultz. On deviation measures in stochastic integer programming. Oper. Res. Lett., 33(5):441–449, 2005. [2421] Giovanni Marro and Remo Rossi. Condizioni di convessita` nella programmazione dinamica. Atti, Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 54:604–614 (1974), 1973. [2422] A. Martel and W. Price. Stochastic programming applied to human resource planning. J. Oper. Res. Soc. 32, 187-196, 1981. [2423] Alain Martel. Programme stochastique pour les plans hommes-machines a moyen terme. Revue Franc. Automat. Inform. Rech. operat. 8, V-1, 5-18, 1974. [2424] Alain Martel. A probabilistic assortment problem. INFOR, Can. J. Operat. Res. Inform. Processing 15, 196-203, 1977. [2425] Alain Martel and Ahmad Al-Nuaimi. Tactical manpower planning via programming under uncertainty. Operat. Res. Quart. 24, 571-585, 1973. [2426] Alain Martel and Jean Ouellet. Stochastic allocation of a resource among partially interchangeable activities. Eur. J. Oper. Res. 74, No.3, 528-539, 1994. [2427] K. Marti. Stochastische Programme in normierten Raeumen. (Stochastic programming in normed spaces). In Operations Research-Verfahren 1 130-132 (1971)., 1970. [2428] K. Marti. Konvexitaetsaussagen zum linearen stochastischen Optimierungsproblem. Z. Wahrscheinlichkeitstheorie Verw. Geb. 18, 159-166, 1971.

136 [2429] K. Marti. Entscheidungsprobleme mit linearem Aktionen- und Ergebnisraum. Z. Angew. Math. Mech., 53:T226–T228, 1973. Vortrage¨ der Wissenschaftlichen Jahrestagung der Gesellschaft fur¨ Angewandte Mathematik und Mechanik (Ljubljana, 1972). [2430] K. Marti. Ueber ein Verfahren zur Loesung einer Klasse linearer Entscheidungsprobleme. Z. angew. Math. Mech. 54, Sonderheft, T 247 - T 248, 1974. [2431] K. Marti. Losung¨ stochastischer linearer Programme mit “complete recourse” mittels stochastischer Penalty-Methoden. Z. Angew. Math. Mech., 58(7):T491–T494, 1978. [2432] K. Marti. Diskretisierung stochastischer Programme unter Berucksichtigung¨ der Problemstruktur. Z. Angew. Math. Mech., 59(3):T105–T108, 1979. Vortrage¨ der Wissenschaftlichen Jahrestagung der Gesellschaft fur¨ Angewandte Mathematik und Mechanik, Teil I (Brussels, 1978). [2433] K. Marti. On approximative solutions of stochastic programming problems by means of stochastic dominance and stochastic penalty methods. In Survey of mathematical programming (Proc. Ninth Internat. Math. Programming Sympos., Budapest, 1976), Vol. 2, pages 117–127, Amsterdam, 1979. North-Holland. [2434] K. Marti. On accelerations of the convergence in random search methods. Methods Oper. Res. 37, 391-406, 1980. [2435] K. Marti. On controlled random search procedures. In Control applications of nonlinear programming and optimization, Coll. Pap., 2nd IFAC Workshop, Oberpfaffenhofen/Ger. 1980, 214-223, 1980. [2436] K. Marti. Random search in optimization problems as a stochastic decision process (adaptive random search). Methods Oper. Res. 36, 223-234, 1980. [2437] K. Marti. Stochastic dominance and the construction of descent directions in stochastic programs having a discrete distribution., 1980. [2438] K. Marti. Stochastische Dominanz und Konstruktion von Abstiegsrichtungen in stochastischen Programmen bei Verteilungs-Symmetrien., 1980. [2439] K. Marti. On stochastic dominance and the construction of directions of decrease in stochastic programs having a discrete distribution. Methods Oper. Res. 41, 175-178, 1981. [2440] K. Marti. Ueber die Berechnung von Abstiegsrichtungen in Stochastischen Linearen Programmen bei Verteilungsinvarianz. Z. Angew. Math. Mech. 61, T341 - T343, 1981. [2441] K. Marti. Minimizing noisy objective functions by random search methods. Z. Angew. Math. Mech. 62, T377 - T380, 1982. [2442] K. Marti. On the construction of descent directions in stochastic programs having a discrete distribution. Z. Angew. Math. Mech., 64(5):336–338, 1984. [2443] K. Marti. Computation of descent directions in stochastic optimization problems with invariant distributions. Z. Angew. Math. Mech., 65(8):355–378, 1985. [2444] K. Marti. Construction of descent directions in stochastic programs having a discrete distribution. II. Z. Angew. Math. Mech., 67(5):T408–T410, 1987. [2445] K. Marti. Descent stochastic quasigradient methods. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 393–401. Springer, Berlin, 1988. [2446] K. Marti. Optimal semi-stochastic approximation procedures. II. Z. Angew. Math. Mech., 69(4):T67–T69, 1989.

137 [2447] K. Marti. Optimal semistochastic approximation. In Computing and computers for control systems (Paris, 1988), volume 4 of IMACS Ann. Comput. Appl. Math., pages 409–415, Basel, 1989. Baltzer. [2448] K. Marti. Computation of efficient solutions of stochastic optimization problems with applications to regression and scenario analysis. In Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, volume 6 of Theory Decis. Lib. Ser. D System Theory Knowledge Engrg. Probl. Solving, pages 163–188. Kluwer Acad. Publ., Dordrecht, 1990. [2449] K. Marti. Stochastic optimization methods in structural mechanics. Z. Angew. Math. Mech., 70(6):T742–T745, 1990. Bericht uber¨ die Wissenschaftliche Jahrestagung der GAMM (Karlsruhe, 1989). [2450] K. Marti. Stochastic programming: numerical solution techniques by semi-stochastic approximation methods. In Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, volume 6 of Theory Decis. Lib. Ser. D System Theory Knowledge Engrg. Probl. Solving, pages 23–43. Kluwer Acad. Publ., Dordrecht, 1990. [2451] K. Marti. Computation of efficient solutions of discretely distributed stochastic optimization problems. Z. Oper. Res., 36(3):259–294, 1992. [2452] K. Marti. Semi-stochastic approximation by the response surface methodology (RSM). Optimiza- tion, 25(2-3):209–230, 1992. [2453] K. Marti. Stochastic optimization in structural design. Z. Angew. Math. Mech., 72(6):T452–T464, 1992. Bericht uber¨ die Wissenschaftliche Jahrestagung der GAMM (Krakow,´ 1991). [2454] K. Marti, editor. Stochastic Optimization. Numerical Methods and Technical Applications. Springer, Berlin, 1992. LN in Economics and Math. Systems 379. [2455] K. Marti. Satisficing techniques in stochastic linear programming. Optimization, 31(4):359–384, 1994. [2456] K. Marti. Differentiation formulas for probability functions: the transformation method. Math. Programming, 75(2, Ser. B):201–220, 1996. Approximation and computation in stochastic programming. [2457] K. Marti. Path planning for robots under stochastic uncertainty. Optimization, 45(1-4):163–195, 1999. Dedicated to the memory of Professor Karl-Heinz Elster. [2458] K. Marti. Stochastic programming methods in adaptive optimal trajectory planning for robots. ZAMM Z. Angew. Math. Mech., 82(11-12):795–809, 2002. 4th GAMM-Workshop “Stochastic Models and Control Theory” (Lutherstadt Wittenberg, 2001). [2459] K. Marti and E. Fuchs. On the convergence rate of semistochastic approximation procedures. Z. Angew. Math. Mech., 65(5):315–317, 1985. [2460] K. Marti and E. Fuchs. Computation of descent directions and efficient points in stochastic optimization problems without using derivatives. Math. Programming Stud., 28:132–156, 1986. Stochastic programming 84. II. [2461] K. Marti and E. Fuchs. Rates of convergence of semistochastic approximation procedures for solving stochastic optimization problems. Optimization, 17(2):243–265, 1986. [2462] K. Marti and E. Plochinger.¨ Optimal semi-stochastic approximation procedures. Z. Angew. Math. Mech., 68(5):T441–T443, 1988. [2463] K. Marti and E. Plochinger.¨ Optimal step sizes in semi-stochastic approximation procedures. I. Optimization, 21(1):123–153, 1990.

138 [2464] K. Marti and E. Plochinger.¨ Optimal step sizes in semistochastic approximation procedures. II. Optimization, 21(2):281–312, 1990. [2465] K. Marti and R.-J. Riepl. Optimale Portefeuilles mit stabil verteilten Renditen. Z. Angew. Math. Mech., 57(5):T337–T339, 1977. [2466] K. Marti and G. L. Tret0yakov. An algorithm for the approximate solution of the maximization problem for a probability function on the basis of a star-shaped approximation. [2467] Kurt Marti. Konvexitatsaussagen¨ zum linearen stochastischen Optimierungsproblem. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 18:159–166, 1971. [2468] Kurt Marti. Entscheidungsprobleme mit linearem Aktionen- und Ergebnisraum. Z. Wahrschein- lichkeitstheorie und Verw. Gebiete, 23:133–147, 1972. [2469] Kurt Marti. Approximationen der Entscheidungsprobleme mit linearer Ergebnisfunktion und pos- itiv homogener, subadditiver Verlustfunktion. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 31:203–233, 1974/75. [2470] Kurt Marti. Approximations to gradients in stochastic programming. Bull. Inst. Internat. Statist., 46(4):137–140 (1976), 1975. [2471] Kurt Marti. Convex approximation of stochastic optimization problems. In Operations Research Verfahren, Band XX, pages 66–76, Meisenheim am Glan, 1975. Hain. [2472] Kurt Marti. Approximations to stochastic optimization problems. In Optimization and operations research (Proc. Conf., Oberwolfach, 1975), pages 201–213. Lecture Notes in Econom. Math. Systems, Vol. 117, Berlin, 1976. Springer. [2473] Kurt Marti. Stochastische Dominanz und stochastische lineare Programme. In VIII. Oberwolfach- Tagung uber¨ Operations Research (1976), Operations Res. Verfahren, XXIII, pages 141–160. Hain, Konigstein/Ts.,¨ 1977. [2474] Kurt Marti. On stochastic dominance relations in stochastic programming. In Transactions of the Eighth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Prague, 1978), Vol. B, pages 35–44. Reidel, Dordrecht, 1978. [2475] Kurt Marti. Stabilitaet approximativer Loesungen stochastischer Programme bei Variationen der Parameterverteilung P. In Oper. Res. Verf. 29, 2nd Symp. Oper. Res., Teil 2, Aachen 1977, 657-671 , 1978. [2476] Kurt Marti. Stochastic linear programs with random data having stable distributions. In Optimiza- tion techniques (Proc. 8th IFIP Conf., Wurzburg,¨ 1977), Part 2, pages 76–86. Lecture Notes in Control and Information Sci., Vol. 7, Berlin, 1978. Springer. [2477] Kurt Marti. Approximationen stochastischer Optimierungsprobleme, volume 43 of Mathematical Systems in Economics. Verlag Anton Hain, Konigstein/Ts.,¨ 1979. [2478] Kurt Marti. On solutions of stochastic programming problems by descent procedures with stochastic and deterministic directions. In Third Symposium on Operations Research (Univ. Mannheim, Mannheim, 1978), Section 3, volume 33 of Operations Res. Verfahren, pages 281–293. Hain, Konigstein/Ts.,¨ 1979. [2479] Kurt Marti. Approximations to stochastic optimization problems. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 159–166, London, 1980. Academic Press. [2480] Kurt Marti. On accelerations of the convergence in random search methods. Mitteilung aus dem forschungsschwerpunkt simulation und optimierung deterministischer und stochastischer dynamischer systeme, Hochschule der Bundeswehr Muenchen, Neubibierg, 1980.

139 [2481] Kurt Marti. Solving stochastic linear programs by semistochastic approximation algorithms. In Recent results in stochastic programming (Proc. Meeting, Oberwolfach, 1979), volume 179 of Lecture Notes in Econom. and Math. Systems, pages 191–213. Springer, Berlin, 1980. [2482] Kurt Marti. On accelerations of stochastic gradient methods by using more exact gradient estima- tions. In X symposium on operations research, Part I, Sections 1–5 (Munich, 1985), volume 53 of Methods Oper. Res., pages 327–336. Athenaum/Hain/Hanstein,¨ Konigstein/Ts.,¨ 1986. [2483] Kurt Marti. Optimally controlled semi-stochastic approximation procedures. In Okonomie¨ und Mathematik, pages 216–230, Berlin, 1987. Springer. [2484] Kurt Marti. Descent directions and efﬁcient solutions in discretely distributed stochastic programs, volume 299 of Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin, 1988. [2485] Kurt Marti. Stochastic optimization methods in engineering. In System modelling and optimization (Prague, 1995), pages 75–87. Chapman & Hall, London, 1996. [2486] Kurt Marti, editor. Structural reliability and stochastic structural optimization. Physica-Verlag, Heidelberg, 1997. Math. Methods Oper. Res. 46 (1997), no. 3. [2487] Kurt Marti. Adaptive optimal stochastic trajectory planning and control (AOSTPC) for robots. Stochastic Programming E-Print Series, http://www.speps.org, 2000. [2488] Kurt Marti, editor. Numerical methods for stochastic optimization and real-time control of robots. Gordon and Breach Science Publishers, Yverdon, 2000. Selected papers from Section 14 on Stochastic Optimization of the 1998 Munich Stochastics Days and the DFG-Workshop on Real- time Control of Robots held in Neubiberg/Munich, March 22–27, 1998, Optimization 47 (2000), no. 3-4. [2489] Kurt Marti. Stochastic optimization methods in robust adaptive control of robots. In Online optimization of large scale systems, pages 545–577. Springer, Berlin, 2001. [2490] Kurt Marti. Robust optimal design: a stochastic optimization problem. In Stochastic optimization techniques (Neubiberg/Munich, 2000), volume 513 of Lecture Notes in Econom. and Math. Systems, pages 35–55. Springer, Berlin, 2002. [2491] Kurt Marti, editor. Stochastic optimization techniques, volume 513 of Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin, 2002. Numerical methods and technical applications, Including papers from the 4th GAMM/IFIP Workshop held at the Federal Armed Forces University Munich, Neubiberg/Munich, June 27–29, 2000. [2492] Kurt Marti. Stochastic Optimization Methods. Springer, 2005. [2493] Kurt Marti and Peter Kall, editors. Stochastic programming, volume 423 of Lecture Notes in Economics and Mathematical Systems, Berlin, 1995. Springer-Verlag. Numerical techniques and engineering applications. [2494] Kurt Marti and Peter Kall, editors. Stochastic programming methods and technical applications, Berlin, 1998. Springer-Verlag. [2495] Olivier Martin, Steve W. Otto, and Edward W. Felten. Large-step Markov chains for the TSP incorporating local search heuristics. Oper. Res. Lett., 11(4):219–224, 1992. [2496] F. Martinelli. Stochastic comparison algorithm for discrete optimization with estimation of time- varying objective functions. J. Optim. Theory Appl., 103(1):137–159, 1999. [2497] Yukihiro Maruyama. Positively bitone sequential decision process. In Nonlinear analysis and convex analysis, pages 341–353. Yokohama Publ., Yokohama, 2007.

140 [2498] J.L. Maryak. Some guidelines for using iterate averaging in stochastic approximation. In Proceed- ings of the IEEE Conference on Decision and Control, pages 2287–2290, 1997. [2499] J.L. Maryak and D.C Chin. Stochastic approximation for global random optimization. In Proceed- ings of the American Control Conference, pages 3294–3298, 2000. [2500] J.L. Maryak, R.H. Smith, and R.L. Winslow. Modeling cardiac ion channel conductivity: model fitting via simulation. In Proceedings of the Winter Simulation Conference, eds. D.J. Medeiros and E.F. Watson, pages 1587–1590, 1998. [2501] S.F. Masri, G.A. Bekey, T.K. Caughey, and E. Van de Velde. Adaptive stochastic optimization using multiprocessors. Appl. Math. Comput., 72(2-3):225–257, 1995. [2502] P. Masse.´ Les Reserves´ et la Regulation´ de l’Avenir dans la vie Economique´ . Hermann, Paris, 1946. vol I and II. [2503] Rudolf Mathar and Antanas Zilinskas.ˇ On global optimization in two-dimensional scaling. Acta Appl. Math., 33(1):109–118, 1993. Stochastic optimization. [2504] V.John Mathews and Sung Ho Cho. Improved convergence analysis of stochastic gradient adaptive filters using the sign algorithm. IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 450-454, 1987. [2505] Jirˇí Matousek.ˇ Lower bounds for a subexponential optimization algorithm. Random Structures Algorithms, 5(4):591–607, 1994. [2506] T.H. Mattheiss and Brian K. Schmidt. Computational results on an algorithm for finding all vertices of a polytope. Math. Programming, 18(3):308–329, 1980. [2507] Josef Matyas. Das zufaellige Optimierungsverfahren und seine Konvergenz. (A random optimization method and her convergence). In 5th internat. Analogue Comput. Meet. Lausanne 1967, Proc., 540-544 , 1968. [2508] Jerrold H. May and Robert L. Smith. Random polytopes: their definition, generation and aggregate properties. Math. Programming, 24(1):39–54, 1982. [2509] J. Mayer. On the STABIL stochastic programming model. Alkalmazott Mat. Lapok 2, 171-187, 1976. [2510] J. Mayer. A nonlinear programming method for the solution of a stochastic programming model of A. Prekopa.´ In Survey of mathematical programming (Proc. Ninth Internat. Math. Programming Sympos., Budapest, 1976), Vol. 2, pages 129–139. North-Holland, Amsterdam, 1979. [2511] J. Mayer. A nonlinear programming method for the solution of a stochastic programming model of A. Prekopa.´ Tanulmanyok—MTA´ Szamit´ astech.´ Automat. Kutato´ Int. Budapest, 167:31–48, 1985. Studies in applied stochastic programming, I. [2512] J. Mayer. Probabilistic constrained optimization—a brief summary on theory and algorithms. In- vestigacion´ Oper., 14(2-3):162–174, 1993. Workshop on Stochastic Optimization: the State of the Art (Havana, 1992). [2513] J. Mayer. On the numerical solution of stochastic optimization problems. In System modeling and optimization, volume 199 of IFIP Int. Fed. Inf. Process., pages 193–206. Springer, New York, 2006. [2514] Janos Mayer. Computational techniques for probabilistic constrained optimization problems. In Stochastic optimization. Numerical methods and technical applications, Proc. GAMM/IFIP- Workshop, Neubiberg/Ger. 1990, Lect. Notes Econ. Math. Syst. 379, 141-164, 1992.

141 [2515] Janos´ Mayer. Stochastic linear programming algorithms. Gordon and Breach Science Publishers, Amsterdam, 1998. A comparison based on a model management system. [2516] Janos´ Mayer. On the numerical solution of jointly chance constrained problems. In Probabilistic constrained optimization, volume 49 of Nonconvex Optim. Appl., pages 220–235. Kluwer Acad. Publ., Dordrecht, 2000. [2517] Vladimir Mazalov and Eduard Kochetov. Mate choice and optimal stopping problem. In Probabil- ity theory and mathematical statistics (Tokyo, 1995), pages 317–326. World Sci. Publishing, River Edge, NJ, 1996. [2518] Vl.D. Mazurov. The method of admissible corrections. In Improper optimization problems, Collect. Artic., Sverdlovsk 1982, 11-22 , 1982. [2519] Patrick H. McAllister. Adaptive approaches to stochastic programming. Ann. Oper. Res., 30(1- 4):45–62, 1991. Stochastic programming, Part I (Ann Arbor, MI, 1989). [2520] Edward A. McBean. Stochastic optimization in acid rain management with variable meteorology. In Stochastic optimization. Numerical methods and technical applications, Proc. GAMM/IFIP- Workshop, Neubiberg/Ger. 1990, Lect. Notes Econ. Math. Syst. 379, 165-172, 1992. [2521] Richard P. McLean. Approximation theory for stochastic variational and Ky Fan inequalities in finite dimensions. Ann. Oper. Res., 44(1-4):43–61, 1993. Advances in equilibrium modeling, analysis and computation. [2522] V.G. Medvedev. An algorithm for solving a two-stage problem of linear stochastic programming. Vestnik Beloruss. Gos. Univ. Ser. I Fiz. Mat. Mekh., 1:64–66, 79, 1987. [2523] M.V. Meerov and M.D. Vainstok. Optimization of multiply-connected objects represented by a system of regression equations as a stochastic-programming problem. Autom. Remote Control 34, 1744-1748 translation from Avtom. Telemekh. 1973, No.11, 36-41 (1973)., 1973. [2524] Nicole Megow, Marc Uetz, and Tjark Vredeveld. Models and Algorithms for Stochastic Online Scheduling. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl. de/05031, 2005. [2525] Sanjay Mehortra and Gokhan Ozevin. On the implementation of interior point decomposition algorithms for two-stage stochastic conic. Optimization Online, http://www. optimization-online.org, 2005. [2526] Abraham Mehrez, Buddy L. Myers, and Moutaz J. Khouja. Quality and inventory issues within the newsboy problem. Comput. Oper. Res. 18, No.5, 397-410, 1991. [2527] Abraham Mehrez and Moshe Sniedovich. An analysis of a dynamic project cost problem. J. Oper. Res. Soc. 43, No.6, 591-604, 1992. [2528] Sanjay Mehrotra. Volumetric center method for stochastic convex programs using sampling. Stochastic Programming E-Print Series, http://www.speps.org, 2000. [2529] Sanjay Mehrotra and M. Gokhan Ozevin. Decomposition-based interior point methods for two- stage stochastic convex quadratic programs with recourse. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [2530] Sanjay Mehrotra and M. Gokhan¨ Ozevin.¨ Two-stage stochastic semidefinite programming and decomposition based interior point methods. Stochastic Programming E-Print Series, http:// www.speps.org, 2005. [2531] Aranyak Mehta, Scott Shenker, and Vijay V. Vazirani. Posted price profit maximization for multi- cast by approximating fixed points. J. Algorithms, 58(2):150–164, 2006.

142 [2532] V.I. Melesko. Ameliorated adaptation algorithms in problems with uncertainty based upon pseu- doinverse operators theory. Izv. Akad. Nauk SSSR, Tekh. Kibernet. 1978, No.2, 39-52, 1978. [2533] Jose Luis Menaldi. Stochastic dynamic programming. Cuad. Inst. Mat. “Beppo Levi” 16, 101 p., 1988. [2534] Roy Mendelssohn. Pareto optimal policies for harvesting with multiple objectives. Math. Biosci. 51, 213-224, 1980. [2535] Marta Susana Mendiondo and Richard H. Stockbridge. Approximation of infinite-dimensional linear programming problems which arise in stochastic control. SIAM J. Control Optim., 36(4):1448– 1472 (electronic), 1998. [2536] Fan-wen Meng and Hui-fu Xu. Exponential convergence of sample average approximation methods for a class of stochastic mathematical programs with complementarity constraints. J. Comput. Math., 24(6):733–748, 2006. [2537] Fanwen Meng and Huifu Xu. A regularized sample average approximation method for stochastic mathematical programs with nonsmooth equality constraints. SIAM J. Optim., 17(3):891–919 (electronic), 2006. [2538] William Menke. Geophysical data analysis: discrete inverse theory. Rev. ed. International Geo- physics Series 45. Academic Press, San Diego, CA etc., 1989. [2539] Carl-Heinz Meyer and Holger Knublauch. Parallel iterative proportional fitting. In Operations Research Proceedings 1999 (Magdeburg), pages 142–147, Berlin, 2000. Springer. [2540] Sean P. Meyn. Stability, performance evaluation, and optimization. In Handbook of Markov decision processes, volume 40 of Internat. Ser. Oper. Res. Management Sci., pages 305–346. Kluwer Acad. Publ., Boston, MA, 2002. [2541] Ph. Michel. Programmes mathematiques´ mixtes. Application au principe du maximum en temps discret dans le cas deterministe´ et dans le cas stochastique. RAIRO Rech. Oper.´ , 14(1):1–19, 1980. [2542] Maciej Michniewicz. An application of the Kalman filter for optimization in the presence of noise. Arch. Automat. Telemech., 25(2):167–177, 1980. [2543] Maciej Michniewicz. On the application of static optimization methods to the technological system control in the presence of noise. Podstawy Sterowania 15, 315-334, 1985. [2544] M.V. Mihalevic.ˇ A stochastic search algorithm for the most preferred element of a compact set. Issled. Operatsii i ASU, 15:71–76, 135, 1980. [2545] M.V. Mihalevic and L.B. Koslai. Some questions of stability theory of the stochastic economical models. In Stability problems for stochastic models, Proc. 6th int. Semin., Moscow 1982, Lect. Notes Math. 982, 123-135, 1983. [2546] G. Mihoc and I. Nadejde. Mathematical Programming: Parametric, Nonlinear and Stochastic. Edutura Stiintifica, Bucurest, 1966. (in Rumanian). [2547] G.A. Mikhailov. Minimax theory of Monte Carlo weight methods. Zh. Vychisl. Mat. i Mat. Fiz., 24(9):1294–1302, 1984. [2548] M.V. Mikhalevich. Generalized stochastic method of centers. Cybernetics, 16(2):292–296, 1980. [2549] M.V. Mikhalevich. Stability of stochastic programming methods to stochastic quasigradient computing errors. Cybernetics 16, 434-438 translation from Kibernetika 1980, No.3, 117-119 (1980)., 1981.

143 [2550] M.V. Mikhalevich. Estimates for the convergence rate of stochastic methods of search for the most preferable element. Dokl. Akad. Nauk Ukr. SSR, Ser. A 1984, No.5, 74-76, 1984. [2551] M.V. Mikhalevich. Analysis of the error tolerance of stochastic methods to ﬁnd the most preferred element. Cybernetics 21, 324-333 translation from Kibernetika 1985, No.3, 41-48 (1985)., 1985. [2552] M.V. Mikhalevich. Estimates for the rate of convergence of stochastic procedures using averaged descent directions. Kibernetika (Kiev), 2:91–100, 135, 1989. [2553] M.V. Mikhalevich and L.B. Koshlaj. Estimates of stability conditions for stochastic programming methods and search methods for the most preferred element. In Problems of stability of stochastic models, Proc. Semin., Moskva 1981, 81- 91, 1981. [2554] M.V. Mikhalevich and L.B. Koshlaj. Estimates and conditions for stability of stochastic programming methods and methods of search for the most preferable element. J. Sov. Math. 34, 1516-1524, 1986. [2555] V.S. Mikhalevich, A.M. Gupal, and I.V. Bolgarin. Numerical methods for solving nonstationary and limit extremal problems without calculating the gradients. Kibernetika (Kiev), 5:ii, 56–57, 65, 134, 1984. [2556] V.S. Mikhalevich, A.M. Gupal, and V.I. Norkin. Methods of non-convex optimization. (Metody nevypukloj optimizatskii). Ehkonomiko-Matematicheskaya Biblioteka. Moskva: Nauka, 1987. [2557] V.S. Mikhalevich, I.V. Sergienko, and N.Z. Shor. Investigation of optimization methods and their applications. Cybernetics 17, 522-548 translation from Kibernetika 1981, No.4, 89-113 (1981)., 1982. [2558] P. Milde. Zu einer Problemstellung der stochastischen linearen Optimierung Stochastische Ziel- funktion. In 18. internat. wiss. Kolloqu., Ilmenau 1, 55-57, 1973. [2559] Peter Milde. Zu einigen Problemstellungen der stochastischen linearen Optimierung. (On some problems of stochastic linear programming). Wiss. Z. Hochschule Architektur Bauwesen Weimar 18, 73-75, 1971. [2560] Peter Milde. Stochastische lineare Optimierung. I. Wiss. Z. Hochschule Architektur Bauwesen Weimar 20, 531-535, 1973. [2561] Yu.N. Minayev and N.M. Chumakov. Algorithms for solving optimization problems under the inﬂuence of noises. Sov. Autom. Control 12, No.3, 56-61, 1979. [2562] Hisashi Mine, Katsuhisa Ohno, and Masao Fukushima. Decompostion of nonlinear chance- constrained programming problems by dynamic programming. J. Math. Anal. Appl., 56(1):221– 222, 1976. [2563] Julio MirasAmor. Transporte mit zufaelliger Nachfrage. Trabajos Estadist. Investig. operat. 24, Nr. 1/2, 185-197, 1973. [2564] B.M. Mirkin and V.A. Siˇ sljakova.ˇ Optimization and analysis of the sensitivity of continuous stochastic systems with discrete control. In Optimization and adaptive control in large-scale systems (Russian), pages 18–27, 105–106. “Ilim”, Frunze, 1980. [2565] Leonard J. Mirman. One sector economic growth and uncertainty: A survey. In Stochastic programming, Proc. int. Conf., Oxford 1974, 537-567, 1980. [2566] Leonard J. Mirman and Daniel F. Spulber. Fishery regulation with harvest uncertainty. Int. Econ. Rev. 26, 731-746, 1985.

144 [2567] A. A. Mironov, A. A. Sokolov, and V. I. Tsurkov. On the probabilistic properties of random transportation matrices consisting of zeros and ones. Izv. Akad. Nauk Teor. Sist. Upr., (6):102–113, 2001. [2568] F. Mirozakhmedov and M.V. Mikhalevich. Applied Aspects of Stochastic Programming. Maorif, Dushanbe, 1989. (in Russian). [2569] F. Mirzoahmedov and V.L. Petrenko. A dynamic problem of inventory planning with random demand. In Methods in operations research and reliability theory in systems of analysis (Russian), pages 89–94, 103, Kiev, 1979. Akad. Nauk Ukrain. SSR Inst. Kibernet. [2570] F. Mirzoahmedov and T.G. Timosenko.ˇ An approach to the solution of the problem of control of the operation of a single reservoir. Akad. Nauk Ukrain. SSR Inst. Kibernet. Preprint, 13:45–51, 55, 1979. Stochastic optimization models. [2571] A.I. Mirzoakhmedov and A.I. Yastremskij. Numerical solution methods and methods of economic and mathematical analysis of stochastic resource planning problems. Methods of qualitative analysis. Issled. Oper. ASU 20, 3-9, 1982. [2572] F. Mirzoakhmedov. A three-stage problem of stochastic programming and the method of its solution. Dokl. Akad. Nauk Tadzhik. SSR, 23(12):694–697, 1980. [2573] F. Mirzoakhmedov. Methods of decomposition constructed on the basis of numerical algorithms of stochastic programming. Dokl. Akad. Nauk Tadzhik. SSR, 27(9):495–499, 1984. [2574] F. Mirzoakhmedov. Some numerical methods for solving two-stage problems of stochastic programming. Kibernetika (Kiev), 6:124–125, 1984. [2575] F. Mirzoakhmedov. An optimization problem in queueing theory and a numerical solution method. Cybernetics 26, No.3, 405-409 translation from Kibernetika 1990, No.3, 73-75 (1990)., 1990. [2576] F. Mirzoakhmedov. Mathematical models and methods for production control taking random factors into account. (Matematicheskie modeli i metody upravleniya proizvodstvom s uchetom slucha- jnykh faktorov). Naukova Dumka, Kiev, 1991. [2577] F. Mirzoakhmedov and A. Gafforov. Stochastic penalty method for the solution of problems with probabilistic constraints. Dokl. Akad. Nauk Tadzhik. SSR, 26(12):761–763, 1983. [2578] F. Mirzoakhmedov and I.N. Kurcheryavaya. Projection algorithm on a multidimensional simplex. Issled. Oper. ASU 23, 59-64, 1984. [2579] F. Mirzoakhmedov and M.V. Mikhalevich. Modeling of optimal cultivated land distribution by means of a multistage stochastic programming problem. Ekonom.` i Mat. Metody, 18(5):918–922, 1982. [2580] F. Mirzoakhmedov and M.V. Mikhalevich. The stochastic quasigradient projection method. Cy- bernetics 19, 566-575 translation from Kibernetika 1983, No.4, 103-109 (1983)., 1983. [2581] F. Mirzoakhmedov, V.V. Mova, and L.V. Sirenko. Numerical methods of stochastic programming in the optimization of mass service systems. Dokl. Akad. Nauk Tadzh. SSR 23, 625-628, 1980. [2582] F. Mirzoakhmedov and V.L. Petrenko. Stochastic programming problems associated with adaptive production planning. Cybernetics, 17(1):107–116, 1981. [2583] F. Mirzoakhmedov and S.P. Uryas’ev. Adaptive step regulation for a stochastic optimization algorithm. Zh. Vychisl. Mat. i Mat. Fiz., 23(6):1314–1325, 1983. [2584] F. Mirzoakhmedov and A.I. Yastremskii. Numerical methods of solution and methods of mathematical-economic analysis of stochastic problems of inventory planning. Methods of qualitative analysis. Issled. Operatsii i ASU, 20:3–9, 1982.

145 [2585] F. Mirzoakhmedov and A.I. Yastremskii. Numerical methods of solution and methods of mathematical-economic analysis of stochastic problems of inventory planning. Numerical methods of solution. Issled. Operatsii i ASU, 19:3–9, 1982. [2586] F.M. Mirzoakhmedov and V.B. Barinov. On a queueing problem. Dokl. Akad. Nauk Tadzh. SSR 33, No.9, 590-592, 1990. [2587] D. Mitra. Analytical results on the use of reduced models in the control of linear dynamical systems. Proc. Inst. Elec. Engrs., 116:1439–1444, 1969. [2588] Gautam Mitra, Harvey J. Greenberg, Freerk A. Lootsma, Marcel J. Rijckaert, and Hans J. Zimmer- mann, editors. Mathematical models for decision support. (Proceedings of the NATO Advanced Study Institute held in Val d’Isere, France, July 26-August 6, 1987). NATO Scientific Affairs Divi- sion, Brussels (Belgium). NATO ASI Series, F, 48. Berlin etc.: Springer-Verlag, 1988. [2589] Yu. I. Mitrofanov and N. V. Yudaeva. Methods for determining optimal routing parameters in queueing networks. Avtomat. i Telemekh., (8):109–117, 2001. [2590] Sanjoy K. Mitter and Pal Toldalagi. Variable metric methods and filtering theory. In Recent developments in variable structure systems, economics and biology (Proc. US-Italy Sem., Taormina, 1977), volume 162 of Lecture Notes in Econom. and Math. Systems, pages 214–221. Springer, Berlin, 1978. [2591] Masakiyo Miyazawa. The characterization of the stationary distribution of the supplemented self- clocking jump process. Math. Oper. Res., 16(3):547–565, 1991. [2592] Norihiro Mizuno. Generalized mathematical programming for optimal replacement in a semi- Markov shock model. Oper. Res. 34, 790-795, 1986. [2593] Regina Hunter Mladineo. Stochastic minimization of Lipschitz functions. In Recent advances in global optimization (Princeton, NJ, 1991), Princeton Ser. Comput. Sci., pages 369–383. Princeton Univ. Press, Princeton, NJ, 1992. [2594] Mohammed Mnif and Huyenˆ Pham. Stochastic optimization under constraints. Stochastic Process. Appl., 93(1):149–180, 2001. [2595] Audrius Mockus, Jonas Mockus, and Linas Mockus. Bayesian approach adapting stochastic and heuristic methods of global and discrete optimization. Informatica, 5(1-2):123–166, 1994. [2596] I. Mockus. Bayesian methods of search for an extremum. In Advances in game theory (Proc. Second All-Union Conf., Vilnius, 1971) (Russian), pages 181–186. Izdat. “Mintis”, Vilnius, 1973. [2597] Ionas Mockus. Sufficient conditions for the convergence of one-dimensional Bayesian methods to the global minimum of continuous functions. Teor. Optimal. Reshenii—Trudy Sem. Protsessy Optimal. Upravleniya VI Sektsiya, 6:9–17, 151, 1980. [2598] J. Mockus. On Bayesian methods for seeking the extremal point. In Stochastic programming, Proc. int. Conf., Oxford 1974, 287-299, 1980. [2599] J. Mockus, W. Eddy, A. Mockus, L. Mockus, and G. Reklaitis. Bayesian Heuristic Approach to Discrete and Global Optimization. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997. [2600] J.B. Mockus. On Bayesian methods in nondifferential and stochastic programming. In Stochastic optimization, Proc. Int. Conf., Kiev/USSR 1984, Lect. Notes Control Inf. Sci. 81, 475-486, 1986. [2601] J.B. Mockus and L.J. Mockus. Bayesian approach to global optimization and application to multiobjective and constrained problems. J. Optim. Theory Appl., 70(1):157–172, 1991.

146 [2602] Jonas Mockus. On Bayesian methods for seeking the extremum and their application. In Inf. Process. 77, Proc. IFIP Congr., Toronto 1977, 195-200, 1977. [2603] Jonas Mockus. Bayesian approach to global optimization, volume 37 of Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht, 1989. Theory and applications, With a 5.25-inch IBM PC floppy disk. [2604] Jonas Mockus. Application of Bayesian approach to numerical methods of global and stochastic optimization. J. Global Optim., 4(4):347–365, 1994. [2605] Jonas Mockus. Average complexity and the Bayesian heuristic approach to discrete optimization. Informatica, 6(2):193–224, 1995. [2606] Jonas Mockus. A set of examples of global and discrete optimization. Kluwer Academic Publishers, Dordrecht, 2000. Applications of Bayesian heuristic approach. [2607] Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, and Gintaras Reklaitis. Bayesian heuristic approach to discrete and global optimization, volume 17 of Nonconvex Optimization and its Applications. Kluwer Academic Publishers, Dordrecht, 1997. With 2 IBM-PC floppy-disks (3.5 inch; HD), Algorithms, visualization, software, and applications. [2608] Jonas Mockus and Henrikas Kuryla. “Learning” Bayesian heuristics in flow-shop problem. Infor- matica, 6(3):289–298, 1995. [2609] Jonas Mockus, Audris Mockus, and Linas Mockus. Bayesian approach for randomization of heuristic algorithms of discrete programming. In Randomization methods in algorithm design (Princeton, NJ, 1997), pages 161–177. Amer. Math. Soc., Providence, RI, 1999. [2610] Jonas Mockus and Elvyra Senkiene.˙ Optimization of a “mixture” of pure heuristics and Monte Carlo algorithms. Informatica (Vilnius), 7(2):167–174, 1996. [2611] Jonas B. Mockus. The Bayesian approach to global optimization. In Statistics: applications and new directions (Calcutta, 1981), pages 405–430. Indian Statist. Inst., Calcutta, 1984. [2612] E. M. Modiano. Derived demand and capacity planning under uncertainty. Operations Research, 35(2):185–197, 1987. [2613] L. Modica. Stochastic homogenization and ergodic theory. In Optimization and related fields (Erice, 1984), volume 1190 of Lecture Notes in Math., pages 359–370. Springer, Berlin, 1986. [2614] R.H. Moehring, F.J. Radermacher, and G. Weiss. Stochastic scheduling problems. I: General strategies. Z. Oper. Res., Ser. A 28, 193-260, 1984. [2615] R.H. Moehring, F.J. Radermacher, and G. Weiss. Stochastic scheduling problems. II: Set strategies. Z. Oper. Res., Ser. A 29, 65-104, 1985. [2616] Rolf H. Moehring and Franz J. Radermacher. Introduction to stochastic scheduling problems. In Contributions to operations research, Proc. Conf., Oberwolfach/Ger. 1984, Lect. Notes Econ. Math. Syst. 240, 72-130, 1985. [2617] C. Mohan and H. T. Nguyen. A fuzzifying approach to stochastic programming. Opsearch, 34(2):73–96, 1997. [2618] C. Mohan and H. T. Nguyen. An interactive satisficing method for solving multiobjective mixed fuzzy-stochastic programming problems. Fuzzy Sets and Systems, 117(1):61–79, 2001. Theme: decision and optimization. [2619] S. R. Mohan, S. K. Neogy, and T. Parthasarathy. Pivoting algorithms for some classes of stochastic games: a survey. Int. Game Theory Rev., 3(2-3):253–281, 2001. Special issue on operations research and game theory with economic and industrial applications (Chennai, 2000).

147 [2620] Ismail Bin Mohd. Interval elimination method for stochastic spanning tree problem. Appl. Math. Comput., 66(2-3):325–341, 1994. [2621] V. V. Moiseenko and V. V. Yatskevich. On global optimization in a class of stochastically unimodal functions. Kibernet. Sistem. Anal., (1):157–166, 190–191, 2000. [2622] Wojciech Molisz. Certain stochastic programming problems. Arch. Automat. i Telemech., 19:17– 25, 1974. [2623] Andris Moller,¨ Werner Romisch,¨ and Klaus Weber. Airline network revenue management by multistage stochastic programming. Stochastic Programming E-Print Series, http://www.speps. org, 2006. [2624] N. P. Moloi and M. M. Ali. An iterative global optimization algorithm for potential energy minimization. Comput. Optim. Appl., 30(2):119–132, 2005. [2625] V.S. Molostvov. Multiple-criteria optimization under uncertainty: Concepts of optimality and sufficient conditions. In Theory and practice of multiple criteria decision making, Collect. Pap. Work- shop, Moscow 1981, 91-105, 1983. [2626] Howard M. Monroe and Jr. Sielken, Robert L. Confidence limits for global optima based on heuristic solutions to difficult optimization problems: a simulation study. Amer. J. Math. Management Sci., 4(1-2):139–167, 1984. Statistics and optimization : the interface. [2627] Kee S. Moon, Farhad Azadivar, and Kyuil Kim. A stochastic optimization of the production speed of robots based on measured geometric and nongeometric errors. Int. J. Prod. Res. 30, No.1, 49-62, 1992. [2628] Chris Morey, John Scales, and Erik S. Van Vleck. A feedback algorithm for determining search parameters for Monte Carlo optimization. J. Comput. Phys., 146(1):263–281, 1998. [2629] Salvatore D. Morgera and Andrew C. Callahan. Source-oriented adaptive beamforming. Circuits Syst. Signal Process. 2, 487-516, 1983. [2630] Hiroaki Morimoto. Optimal switching for alternating processes. Appl. Math. Optimization 16, 1-17, 1987. [2631] Hiroshi Morita and Hiroaki Ishii. A stochastic improvement method for stochastic programming. Comput. Statist. Data Anal., 14(4):477–487, 1992. [2632] Hiroshi Morita and Hiroaki Ishii. An efficient algorithm for a stochastic linear knapsack problem with a single index model. Math. Japon., 38(1):17–25, 1993. [2633] Hiroshi Morita, Hiroaki Ishii, and Toshio Nishida. Confidence region method for a stochastic programming problem. J. Oper. Res. Soc. Japan, 30(2):218–231, 1987. [2634] Hiroshi Morita, Hiroaki Ishii, and Toshio Nishida. Confidence region method for a stochastic linear knapsack programming problem. Math. Japon., 33(4):559–564, 1988. [2635] Hiroshi Morita, Hiroaki Ishii, and Toshio Nishida. Stochastic programming with estimated objective. Tech. Rep. Osaka Univ., 39(1947-1958):1–7, 1989. [2636] Hiroshi Morita, Hiroaki Ishii, and Toshio Nishida. Stochastic linear programming problem with partially estimated constraint. Math. Jap. 35, No.3, 551-559, 1990. [2637] Hiroshi Morita and Lawrence M. Seiford. Characteristics on stochastic DEA efficiency—reliability and probability being efficient. J. Oper. Res. Soc. Japan, 42(4):389–404, 1999. [2638] William J. Morokoff. Generating quasi-random paths for stochastic processes. SIAM Rev., 40(4):765–788 (electronic), 1998.

148 [2639] P.A. Moroz. Continuous optimization stochastic processes as idealized models of procedures for global search optimization. In Random search and pattern recognition (Russian), pages 50–66, 119. “Fan”, Tashkent, 1985. [2640] P.A. Moroz and A.P. Korostelev. Ueber die Ermittlung des bedingten Extremums mit einem Zufalls- Suchverfahren. Avtomatika vycislit. Tehn., Riga 1975, Nr. 2, 36-39, 1975. [2641] P.A. Moroz and A.P. Korostelev. The principle of construction for stochastic optimization procedures under constrained conditions. Avtomat. i Vycisl.ˇ Tehn. (Riga), 3:37–42, 1976. [2642] L.Ju. Morozenskii. On the asymptotic length of a commercial traveller’s path when towns are randomly allocated. Theory Probab. Appl. 19, 798-801 translation from Teor. Verojatn. Primen. 19, 828-831 (1974)., 1974. [2643] J.G. Morris and H.E. Thompson. A note on the ”value” of bounds on EVPI in stochastic programming. Nav. Res. Logist. Q. 27, 165-169, 1980. [2644] A.M. Morshedi. An on-line search for optimum operating conditions of noisy systems. J. Franklin Inst. 310; 89-105, 1980. [2645] D. Morton and E. Popova. Monte carlo simulations for stochastic optimization. In C.A. Floudas and P.M. Pardalos, editors, Encyclopedia of Optimization. Kluwer Academic Publishers, 2001. [2646] David P. Morton. An enhanced decomposition algorithm for multistage stochastic hydroelectric scheduling. Ann. Oper. Res., 64:211–235, 1996. Stochastic programming, algorithms and models (Lillehammer, 1994). [2647] David P. Morton. Stopping rules for a class of sampling-based stochastic programming algorithms. Oper. Res., 46(5):710–718, 1998. [2648] David P. Morton and Guzin Bayraksan. Assessing Solution Quality in Stochastic Programs. In S. Albers, R.H. Mohring,¨ G.Ch. Pﬂug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algo- rithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [2649] David P. Morton, Feng Pan, and Kevin J. Saeger. Models for nuclear smuggling interdiction. Stochastic Programming E-Print Series, http://www.speps.org, 2006. [2650] David P. Morton, Javier Salmeron,´ and R. Kevin Wood. A stochastic program for optimizing military sealift subject to attack. Stochastic Programming E-Print Series, http://www.speps. org, 2003. [2651] David P. Morton and R. Kevin Wood. Restricted-recourse bounds for stochastic linear programming. Oper. Res., 47(6):943–956, 1999. [2652] D.P. Morton, F. Pan, and K.J. Saeger. Models for nuclear smuggling interdiction. IIE Transactions on Operations Engineering, 38:3–14, 2007. [2653] D.P. Morton and E. Popova. A Bayesian stochastic programming approach to an employee scheduling problem. IIE Transactions on Operations Engineering, 36:155–167, 2003. [2654] D.P. Morton, E. Popova, and I. Popova. Efﬁcient fund of hedge funds construction under downside risk measures. Journal of Banking and Finance, 30:503–518, 2006. [2655] D.P. Morton, E. Popova, I. Popova, and M. Zhong. Optimizing benchmark-based utility functions. Bulletin of the Czech Econometric Society, 10:1–18, 2003. [2656] D.P. Morton and R.K. Wood. On a stochastic knapsack problem and generalizations. In D.L. Woodruff, editor, Advances in Computational and Stochastic Optimization, Logic Programming, and Heuristic Search: Interfaces in Computer Science and Operations Research, pages 149–168. Kluwer Academic Publishers, Boston, 1998.

149 [2657] M. Mostaghimi. Monetary policy simulation using SPSA-based neural networks. In Proceedings of the IEEE Conference on Decision and Control, pages 492–497, 1997. [2658] I. B. Motskus. Bayesian methods of optimization of continuous functions, computed with errors. In Mathematical models in immunology and medicine (Russian) (Moscow, 1982), pages 257–261. “Mir”, Moscow, 1986. [2659] Ionas Motskus and Linas Motskus. A Bayesian approach to global optimization, and applications. Teor. Optimal. Reshenii, 12:54–70, 1987. [2660] Ionas Motskus, Lolita Zhukauskaite, and Tautvidas Lideikis. A Bayesian approach to local optimization. Teor. Optimal. Reshenii, 12:71–79, 1987. [2661] Jonas Motskus. Sufﬁcient conditions for the convergence of Bayesian methods to the global minimum. In Numer. Optim. Meth. Appl., Optim. Decis. Theory, Issue 4, Inst. Math. Cybern. Acad. Sci. Lith. SSR, 67-88, 1978. [2662] P.H. Mueller. Probleme der Steuerung stochastischer Prozesse. Mitt. Math. Ges. DDR 1977, No.1, 57-74, 1977. [2663] P.Heinz Mueller and Eckhard Platen. Das asymptotische Verhalten optimaler Rangstrategien beim ”Problem der besten Wahl”. Wiss. Z. Tech. Univ. Dres. 24, 933-937, 1975. [2664] Rahul Mukerjee. Univariate stochastic programming with random decision variable. J. Oper. Res. Soc., 33(10):957–959, 1982. [2665] Rahul Mukerjee. Optimal randomized decision rule in univariate stochastic programming. Opsearch, 21(3):179–182, 1984. [2666] Eh.A. Mukhacheva, I.A. Solomeshch, and N.I. Solomeshch. Optimization of linear stochastic cut- out according to the cost criterion. Optimizatsiya 44(61), 56-63, 1988. [2667] Eh.A. Mukhacheva and N.I. Solomeshch. The problem of stochastic linear cut-out. Optimizatsiya 36(53), 49-55, 1985. [2668] S.P. Mukherjee. Mixed strategies in chance-constrained programming. J. Oper. Res. Soc., 31(11):1045–1047, 1980. [2669] P. Heinz Muller,¨ Andreas Hahnewald-Busch, Peter Neumann, and Volker Nollau. Optimierung mittels stochastischer Suchverfahren. Wiss. Z. Tech. Univ. Dresden, 32(1):69–75, 1983. [2670] Peter Muller.¨ Simulation-based optimal design. In Bayesian statistics, 6 (Alcoceber, 1998), pages 459–474. Oxford Univ. Press, New York, 1999. [2671] Peter Muller¨ and Giovanni Parmigiani. Optimal design via curve ﬁtting of Monte Carlo experiments. J. Amer. Statist. Assoc., 90(432):1322–1330, 1995. [2672] John M. Mulvey and Andrzej Ruszczynski.´ A diagonal quadratic approximation method for linear multistage stochastic programming problems. In System modelling and optimization (Zurich, 1991), volume 180 of Lecture Notes in Control and Inform. Sci., pages 588–597. Springer, Berlin, 1992. [2673] John M. Mulvey and Andrzej Ruszczynski.´ A new scenario decomposition method for large-scale stochastic optimization. Oper. Res., 43(3):477–490, 1995. [2674] John M. Mulvey, Robert J. Vanderbei, and Stavros A. Zenios. Robust optimization for large-scale systems. Operations Research, 43:264–281, 1995.

150 [2675] John M. Mulvey and Hercules Vladimirou. Evaluation of a parallel hedging algorithm for stochastic network programming. In R. Sharda, B. L. Golden, E. Wasil, O. Balci, and W. Stewart, editors, Impacts of Recent Computer Advances on Operations Research, pages 106–119. North-Holland, New York, 1989. [2676] John M. Mulvey and Hercules Vladimirou. Stochastic network optimization models for investment planning. Ann. Oper. Res. 20, 187-217, 1989. [2677] John M. Mulvey and Hercules Vladimirou. Applying the progressive hedging algorithm to stochastic generalized networks. Ann. Oper. Res., 31(1-4):399–424, 1991. Stochastic programming, Part II (Ann Arbor, MI, 1989). [2678] John M. Mulvey and Hercules Vladimirou. Solving multistage stochastic networks: An application of scenario generation. Networks, 21:619–643, 1991. [2679] John M. Mulvey and Hercules Vladimirou. Stochastic network programming for ﬁnancial planning problems. Manage. Sci. 38, No.11, 1642-1664, 1992. [2680] Cecile´ Murat and Vangelis Th. Paschos. Probleme` du stable probabiliste. C.R. Acad. Sci. Paris Ser.´ I Math., 321(4):495–498, 1995. [2681] Cecile´ Murat and Vangelis Th. Paschos. The probabilistic minimum vertex-covering problem. Int. Trans. Oper. Res., 9(1):19–32, 2002. [2682] E.I. Murga and N.V. Roenko. The direct method for solution and analysis of a two-stage linear stochastic problem. In Methods and software for optimization, modeling and construction of systems, Collect. Sci. Works, Kiev, 73-81, 1988. [2683] Yoshisada Murotsu and Fuminori Oba. A study on linear programming under uncertainty. Bull. Univ. Osaka Prefecture Ser. A, 23:61–74, 1974. [2684] Yoshisada Murotsu, Fuminori Ohba, and Tsutomu Abe. A method of determining tolerances for the control variables in stochastic linear programming problems. Systems and Control, 18:219–225, 1974. [2685] Yoshisada Murotsu, Fuminori Ohba, and Hiroshi Itoh. On a solution of stochastic nonlinear programming problems. Bull. Univ. Osaka Prefecture Ser. A, 20(1):97–108, 1971. [2686] Robert A. Murphey. An approximate algorithm for a weapon target assignment stochastic program. In Approximation and complexity in numerical optimization (Gainesville, FL, 1999), volume 42 of Nonconvex Optim. Appl., pages 406–421. Kluwer Acad. Publ., Dordrecht, 2000. [2687] F.H. Murphy, S. Sen, and A.L. Soyster. Electric utility capacity expansion planning with uncertain load forecasts. AIIE Transaction 14:52-59, 1982. [2688] Michael R. Murr and Andras´ Prekopa.´ Solution of a product substitution problem using stochastic programming. In Probabilistic constrained optimization, volume 49 of Nonconvex Optim. Appl., pages 252–271. Kluwer Acad. Publ., Dordrecht, 2000. [2689] D.A. Murtazin and A.S. Poznyak. Recurrent algorithms for search optimization under conditions of relative noise. I. Limit possibilities. Avtomat. i Telemekh., 9:95–109, 1987. [2690] D.A. Murtazin and A.S. Poznyak. Recurrent algorithms for search optimization under conditions of relative noise. II. Optimal search procedures. Avtomat. i Telemekh., 10:89–96, 1987. [2691] D.A. Murtazin and A.S. Poznyak. Recurrent search optimization algorithms in the presence of relative noise. II: Optimal search procedures. Autom. Remote Control 48, No.10, 1343-1349 translation from Avtom. Telemekh. 1987, No.10, 89-96 (1987)., 1987.

151 [2692] Raymond Nadeau and Radu Theodorescu. Restricted Bayes strategies for programs with simple recourse. Oper. Res., 28(3, part 2):777–784, 1980. [2693] Raymond Nadeau and Radu Theodorescu. Restricted Bayes strategies for convex stochastic programs. Rend. Circ. Mat. Palermo (2), 33(1):109–116, 1984. [2694] Raymond Nadeau and Bruno Urli. A fuzzy/stochastic multiobjective linear programming method. In Multiple criteria decision making, Proc. 9th Int. Conf. Theory Appl. Bus. Ind. Gov., Fairfax/VA (USA) 1990, 283-296, 1992. [2695] Raymond Nadeau, Bruno Urli, and Laszlo N. Kiss. PROMISE: A DSS for multiple objective stochastic linear programming problems. Ann. Oper. Res. 51, 45-59, 1994. [2696] Tamas´ Nagy. Stochastic variants of the entropy programming. Alkalmaz. Mat. Lapok, 17(1-2):143– 169 (1994), 1993. [2697] Tamas´ Nagy. A stochastic variant of the transportation problem. Investigacion´ Oper., 15(2-3):191– 205, 1994. [2698] Tamas´ Nagy. Models and algorithms of the entropy programming. Alkalmaz. Mat. Lapok, 22(1):115–134, 2005. [2699] Dania Naja. Convergence faible du recuit simule´ gen´ eralis´ e´ a` temps discret. C. R. Acad. Sci. Paris Ser.´ I Math., 328(12):1213–1218, 1999. [2700] K. Najim, A. Rusnak, A. Meszaros, and M. Fikar. Constrained long-range predictive control based on artiﬁcial neural networks. International Journal of Systems Science, 28:1211–1226, 1997. [2701] Toru¯ Nakai. An optimal assignment problem for multiple objects per period—case of a partially observable Markov chain. Bull. Inform. Cybernet., 31(1):23–34, 1999. [2702] Masao Nakamura. On a class of stochastic optimization problems with a speciﬁed growth pattern. Management Sci., Appl. 20, 236-239, 1973. [2703] A.N. Nakonechnyi. Optimal replacement of systems with respect to turnout. In Mathematical methods for the analysis and optimization of complex systems that function under conditions of uncertainty (Russian), pages 33–40, iii. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1986. [2704] A.N. Nakonechnyi. The method of the small parameter in the analysis of stochastic extremal problems with rare events. In Analysis of stochastic systems by methods in operations research and reliability theory (Russian), pages 29–31, iii. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1987. [2705] A.N. Nakonechnyi. Singularly perturbed stochastic extremal problems. In Mathematical methods for the analysis of complex stochastic systems (Russian), pages 38–44, iii–iv, Kiev, 1988. Akad. Nauk Ukrain. SSR Inst. Kibernet. [2706] A.N. Nakonechnyi. On the method of successive random approximations. Dokl. Akad. Nauk Ukrain. SSR Ser. A, 9:16–18, 85, 1989. [2707] A.N. Nakonechnyi. Extremal problems with rare events. I. Kibernetika (Kiev), 5:55–58, 66, 133, 1990. [2708] A.N. Nakonechnyi. Extremal problems with rare events. II. The method of successive random approximations. Kibernet. Sistem. Anal., 2:33–39, 188, 1992. [2709] A.N. Nakonechnyi. Iterative processes: a survey of the theory of convergence that uses Lyapunov’s second method. Kibernet. Sistem. Anal., 4:66–85, 189, 1994. [2710] A.N. Nakonechnyi. A probability-theoretic analogue of the method of vector Lyapunov functions. Kibernet. Sistem. Anal., 3:110–119, 191, 1994.

152 [2711] A.N. Nakonechnyj. On the method of succesive random approximations. Dokl. Akad. Nauk Ukr. SSR, Ser. A 1989, No.9, 16-18, 1989. [2712] P. Nandakumar, S.M. Datar, and R. Akella. Models for measuring and accounting for cost of conformance quality. Manage. Sci. 39, No.1, 1-16, 1993. [2713] Hiroyuki Narihisa. An algorithm for solving the stochastic programming problem. Mem. Defense Acad., 18(3):151–160, 1978. [2714] Mohammad Naseh and M. M. Khalid. Solution of chance constrained linear programming by ellipsoid method. Pure Appl. Math. Sci., 59(1-2):71–80, 2004. [2715] P. Nash and R.R. Weber. Dominant strategies in stochastic allocation and scheduling problems. In Deterministic and stochastic scheduling, Proc. NATO Adv. Study Res. Inst., Durham/Engl. 1981, 343-353, 1982.

[2716] J. L. Nazareth. The dlp decision support system and its extension to stochastic programming. Optim. Methods Softw., 13(2):117–154, 2000.

[2717] J. L. Nazareth. The DLP decision support system and its extension to stochastic programming. Optim. Methods Softw., 13(2):117–154, 2000. [2718] J.L. Nazareth. Algorithms based upon generalized linear programming for stochastic programs with recourse. In Stochastic programming (Gargnano, 1983), volume 76 of Lecture Notes in Con- trol and Inform. Sci., pages 210–234. Springer, Berlin, 1986. [2719] J.L. Nazareth and R.J.-B. Wets. Algorithms for stochastic programs: the case of nonstochastic tenders. Math. Programming Stud., 28:1–28, 1986. Stochastic programming 84. II. [2720] L. Nazareth. Design and implementation of a stochastic programming optimizer with recourse and tenders. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 273–294. Springer, Berlin, 1988. [2721] L. Nazareth and R.J.-B. Wets. Nonlinear programming techniques applied to stochastic programs with recourse. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 95–121. Springer, Berlin, 1988. [2722] A.V. Nazin. Game approach to the solution of a problem of stochastic programming. Automat. Remote Control, 39(2, part 1):215–223, 1978. [2723] A.V. Nazin. Game problem of adaptive selection of versions and an algorithm for solving it. Autom. Remote Control 45, 1443-1448 translation from Avtom. Telemekh. 1984, No.11, 70-75 (1984)., 1984. [2724] A.V. Nazin. Informational inequalities in the problem of gradient stochastic optimization and optimal realizable algorithms. Autom. Remote Control 50, No.4, 531-540 translation from Avtom. Telemekh. 1989, No.4, 127-138 (1989)., 1989. [2725] T.V. Necaeva. Ueber die Moeglichkeit der Reduktion des Problems der kollektiven Entscheidun- gen zum Mehretappenproblem der stochastischen Programmierung. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1975, Nr. 3, 30-36, 1975. [2726] T.V. Nechayeva. The possibility of reducing a problem of collective decisions to a many-step stochastic programming problem. Engrg. Cybernetics, 13(3):25–31, 1975. [2727] N.A. Nechval’. On a method of stochastic optimization. Probl. Sluchajnogo Poiska 4, 85-94, 1975. [2728] N.A. Nechval’. The synthesis of adaptive control strategies for successive processes in problems of the statistical search for the extremum and in the theory of taking statistical decisions. Probl. Sluchajnogo Poiska 8, 186-236, 1980.

153 [2729] M.C. Nechyba and Y. Xu. Human-control strategy: abstraction, veriﬁcation, and replication. IEEE Control Systems Magazine, 17(5):48–61, 1997. [2730] V.N. Nefedov.¨ Calculating a probabilistic optimization criterion by branch and cut methods. J. Comput. Systems Sci. Internat., 32(6):62–71, 1994. [2731] C.V. Negoita, P. Flondor, and M. Sularia. On fuzzy environment in optimization problems. Econ. Comput. Econ. Cybern. Stud. Res. 1977, 13-24, 1977. [2732] C.V. Negoit¸a and M. Sularia. Optimization in fuzzy environment. In Digital processing and transmission of data and control of processes by means of computers, volume 10 of Probleme de Au- tomat., pages 241–251. Ed. Acad. R.S. Romania,ˆ Bucharest, 1978. [2733] Frederike Neise. Optimization of dispersed generation systems including risk aversion. In CTW2006—Cologne-Twente Workshop on Graphs and Combinatorial Optimization, volume 25 of Electron. Notes Discrete Math., pages 105–106 (electronic). Elsevier, Amsterdam, 2006. [2734] V.V. Nekrutkin and A.S. Tikhomirov. Speed of convergence as a function of given accuracy for random search methods. Acta Appl. Math., 33(1):89–108, 1993. Stochastic optimization. [2735] Z.V. Nekrylova. Ueber die Methode des stochastischen Gradienten im unendlich-dimensionalen Raume. Kibernetika, Kiev 1974, Nr. 1, 142-144, 1974. [2736] Z.V. Nekrylova. Ueber die Konvergenzgeschwindigkeit der Methode des stochastischen Gradien- ten. Kibernetika, Kiev 1975, Nr. 2, 40-43, 1975. [2737] Z.V. Nekrylova. Asymptotic behavior of the stochastic quasigradient method. Kibernetika (Kiev), 3:81–85, 1978. [2738] Z.V. Nekrylova. A method for estimating the unknown parameters of the functional dependence between variables which are observed with noise. Kibernetika (Kiev), 4:61–63, 135, 1987. [2739] Arkadi Nemirovski and Alexander Shapiro. Scenario approximations of chance constraints. Opti- mization Online, http://www.optimization-online.org, 2004. [2740] Arkadi Nemirovski and Alexander Shapiro. Convex approximations of chance constrained programs. SIAM J. Optim., 17(4):969–996 (electronic), 2006. [2741] Arkadi Nemirovski and Alexander Shapiro. On complexity of shmoys - swamy class of two-stage linear stochastic programming problems. Optimization Online, http://www. optimization-online.org, 2006. [2742] A.S. Nemirovskii, B.T. Polyak, and Ya. Z. Tsypkin. Optimal algorithms for stochastic optimization under multiplicative noise. Dokl. Akad. Nauk SSSR, 284(3):564–567, 1985. [2743] A.S. Nemirovskij, B.T. Polyak, and Ya.Z. Tsypkin. Optimum algorithms for stochastic optimization with multiplicative error. Sov. Phys., Dokl. 30, No.9, 744-745 translation from Dokl. Akad. Nauk SSSR 284, No.3 (1988)., 1988. [2744] Yu. Nesterov. Characteristic functions of directed graphs and applications to stochastic equilibrium problems. Optim. Eng., 8(2):193–214, 2007. [2745] Yu. Nesterov and J.-Ph. Vial. Conﬁdence level solutions for stochastic programming. Stochastic Programming E-Print Series, http://www.speps.org, 2000. [2746] Aurel Netea. Sur un probleme de programmation lineaire aleatoire pseudo-booleenne. In Opera- tions research, Proc. 3rd Colloq., Cluj-Napoca/Rom. 1978, 194-198 , 1979. [2747] Serguei Netessine, Gregory Dobson, and Robert A. Shumsky. Flexible service capacity: optimal investment and the impact of demand correlation. Oper. Res., 50(2):375–388, 2002.

154 [2748] Dan Nettleton. Convergence properties of the EM algorithm in constrained parameter spaces. Canad. J. Statist., 27(3):639–648, 1999. [2749] K. Neumann. Dynamische Optimierung und optimale Steuerung in speziellen GERT- Netzplaenen. Wiss. Z., Tech. Hoch-sch. Leipz. 4, 349-355, 1980. [2750] K. Neumann. An optimality equation for stochastic decision networks. Wiss. Z., Tech. Hochsch. Leipz. 8, 79-87, 1984. [2751] Klaus Neumann. Optimal time-cost trade-offs by means of stochastic networks. Methods Oper. Res. 42, 5-16, 1981. [2752] Klaus Neumann. GERT networks with tree structure: Properties, temporal analysis, cost minimization, and scheduling. In Contributions to operations research, Proc. Conf., Oberwolfach/Ger. 1984, Lect. Notes Econ. Math. Syst. 240, 142-158, 1985. [2753] H. Niederreiter. A quasi Monte Carlo method for the approximate computation of the extreme values of a function. In Studies in pure mathematics, Mem. of P. Turan, 523-529, 1983. [2754] H. Niederreiter and P. Peart. A comparative study of quasi - Monte Carlo methods for optimization of functions of several variables. Caribb. J. Math. 1, 27-44, 1982. [2755] Harald Niederreiter. Quasi-Monte Carlo methods for global optimization. In Mathematical statistics and applications, Vol. B (Bad Tatzmannsdorf, 1983), pages 251–267. Reidel, Dordrecht, 1985. [2756] Soren S. Nielsen and Stavros A. Zenios. An investigation of the effect of problem structure on stochastic programming algorithms. In Dongarra, Jack (ed.) et al., Proceedings of the ﬁfth SIAM conference on parallel processing for scientiﬁc computing, held in Houston, TX, USA, March 25- 27, 1991. Philadelphia, PA: SIAM, (ISBN 0-89871-303-X/pbk). 193- 198, 1992. [2757] Soren S. Nielsen and Stavros A. Zenios. A massively parallel algorithm for nonlinear stochastic network problems. Oper. Res. 41, No.2, 319-337, 1993. [2758] Soren S. Nielsen and Stavros A. Zenios. Solving multistage stochastic network programs on massively parallel computers. Math. Programming (Ser. A), 73(3):227–250, 1996. [2759] Soren S. Nielsen and Stavros A. Zenios. A stochastic programming model for funding single premium deferred annuities. Math. Programming (Ser. B), 75(2):177–200, 1996. Approximation and computation in stochastic programming. [2760] Soren S. Nielsen and Stavros A. Zenios. Scalable parallel Benders decomposition for stochastic linear programming. Parallel Comput., 23(8):1069–1088, 1997. [2761] Wojciech Niemiro. Limit distributions of simulated annealing Markov chains. Discuss. Math. Algebra Stochastic Methods, 15(2):241–269, 1995. [2762] Wojciech Niemiro. Tail events of simulated annealing Markov chains. J. Appl. Probab., 32(4):867– 876, 1995. [2763] Peter Nijkamp and Aura Reggiani. Interaction, evolution and chaos in space. Springer-Verlag, Berlin, 1992. [2764] E.G. Nikolaev. Low descent by means of random m-gradient method. Avtomat. vycislit. Tehn., Riga 1970, No.3, 40-46, 1970. [2765] N.D. Nikolaeva. A certain stochastic programming problem. In Mathematical methods for the solution of economic problems (Suppl. to Ekonom.´ i Mat. Metody, Collection No. 3) (Russian), pages 52–58. Izdat. “Nauka”, Moscow, 1972.

155 [2766] Efstratios Nikolaidis and Ricardo Burdisso. Reliability based optimization: A safety index approach. Comput. Struct. 28, No.6, 781-788, 1988. [2767] Jose´ Nino-Mora.˜ Marginal productivity index policies for scheduling restless bandits with switching penalties. In S. Albers, R.H. Mohring,¨ G.Ch. Pﬂug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl. de/05031, 2005. [2768] N.N., editor. Optimization theory and related ﬁelds. Proceedings of a symposium held at the Re- search Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan, November 5-7, 1990. RIMS Kokyuroku. 747. Kyoto: Kyoto University, Research Institute for Mathematical Sciences, iv, 197 p., 1991. [2769] Marie-Cecile´ Noel¨ and Yves Smeers. On the use of nested decomposition for solving nonlinear multistage stochastic programs. In Stochastic programming (Gargnano, 1983), volume 76 of Lec- ture Notes in Control and Inform. Sci., pages 235–246. Springer, Berlin, 1986. [2770] Marie-Cecile´ Noel¨ and Yves Smeers. Nested decomposition of multistage nonlinear programs with recourse. Math. Programming, 37(2):131–152, 1987. [2771] V. Nollau. A stochastic decision model with vector-valued reward. Optimization 16, 733-742, 1985. [2772] V. Nollau and A. Hahnewald-Busch. An approximation procedure for stochastic dynamic programming based on clustering of state and action spaces. Math. Operationsforsch. Statist. Ser. Optim., 10(1):121–130, 1979. [2773] Volker Nollau. Some aspects of vector-valued stochastic dynamic programming. In Markov processes and control theory (Gaußig, 1988), volume 54 of Math. Res., pages 149–157. Akademie- Verlag, Berlin, 1989. [2774] V. I. Norkin and B. O. Onishchenko. Minorant methods of stochastic global optimization. Kibernet. Sistem. Anal., 41(2):56–70, 189, 2005. [2775] V.I. Norkin. Two random search algorithms for the minimization of nondifferentiable functions. In Mathematical methods in operations research and reliability theory (Russian), pages 36–40, Kiev, 1978. Akad. Nauk Ukrain. SSR Inst. Kibernet. [2776] V.I. Norkin. Random generalized-differential functions in the problem of nonconvex nonsmooth stochastic optimization. Kibernetika (Kiev), 6:98–102, 135, 1986. [2777] V.I. Norkin. Random Lipschitz functions. Kibernetika (Kiev), 76(2):66–71, 1986. [2778] V.I. Norkin. Stochastic generalized-differentiable functions in the problem of nonconvex nonsmooth stochastic optimization. Cybernetics 22, No.6, 804-809 translation from Kibernetika 1986, No.6, 98-102 (1986)., 1986. [2779] V.I. Norkin. Stochastic Lipschitz functions. Cybernetics 22, 226-233 translation from Kibernetika 1986, No.2, 66-71, 76 (1986)., 1986. [2780] V.I. Norkin. Optimizatsiya veroyatnostei, volume 89 of Preprint. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1989. [2781] V.I. Norkin. Ustoichivost’ stokhasticheskikh optimizatsionnykh modelei i statisticheskie metody stokhasticheskogo programmirovaniya (po materialam IIASA), volume 89 of Preprint. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1989. [2782] V.I. Norkin. Conditions for and convergence rate of the method of empirical averages in mathematical statistics and stochastic programming. Kibernet. Sistem. Anal., 2:107–120, 190, 1992.

156 [2783] V.I. Norkin, Yu.M. Ermoliev, and A. Ruszczynski. On optimal allocation of indivisibles under uncertainty. Operations Research, 46(3):381–395, 1998. [2784] Vladimir Norkin. Global optimization of probabilities by the stochastic branch and bound method. In Stochastic programming methods and technical applications (Neubiberg/Munich, 1996), pages 186–201. Springer, Berlin, 1998. [2785] Vladimir Norkin and Boris. Onischenko. Minorant methods for stochastic global optimization. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algo- rithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [2786] Vladimir I. Norkin, Georg Ch. Pflug, and Andrzej Ruszczynski.´ A branch and bound method for stochastic global optimization. Math. Programming, 83(3, Ser. A):425–450, 1998. [2787] Alfred L. Norman and David W. Shimer. Risk, uncertainty, and complexity. J. Econ. Dyn. Control 18, No.1, 231-249, 1994. [2788] D.A. Novikov. Optimal stimulation mechanisms in an active system with probabilistic uncertainty. III. Avtomat. i Telemekh., 12:118–123, 1995. [2789] N.M. Novikova. A stochastic quasigradient method for maximin search. Z.ˇ Vycisl.ˇ Mat. i Mat. Fiz., 17(1):91–99, 284, 1977. [2790] N.M. Novikova. A stochastic quasi-gradient method of solving optimization problems in Hilbert space. U.S.S.R. Comput. Math. Math. Phys. 24, No.2, 6-16, 1984. [2791] N.M. Novikova. Stochastic quasigradient method for solving optimization problems in Hilbert space. Zh. Vychisl. Mat. Mat. Fiz. 24, No.3, 348-362, 1984. [2792] N.M. Novikova. Some methods of stochastic programming in Hilbert space. U.S.S.R. Comput. Math. Math. Phys. 25, No.6, 127-138 translation from Zh. Vychisl. Mat. Mat. Fiz. 25, No.12, 1795- 1813 (1985)., 1985. [2793] N.M. Novikova. On stochastic programming in Hilbert space. In Stochastic optimization (Kiev, 1984), volume 81 of Lecture Notes in Control and Inform. Sci., pages 487–495. Springer, Berlin, 1986. [2794] N.M. Novikova. A method of finding a stochastic saddle point. U.S.S.R. Comput. Math. Math. Phys. 29, No.1, 27-34 translation from Zh. Vychisl. Mat. Mat. Fiz. 29, No.1, 39-49 (1989)., 1989. [2795] N.M. Novikova. Some methods for the numerical solution of continuous convex stochastic problems of optimal control. Zh. Vychisl. Mat. i Mat. Fiz., 31(11):1605–1618, 1991. [2796] N.M. Novikova. Iterative stochastic methods for solving variational problems of mathematical physics and operations research. J. Math. Sci., 68(1):1–124, 1994. Analysis, 2. [2797] A. Nowak. On a general dynamic programming problem. Colloq. Math., 37(1):131–138, 1977. [2798] Andrzej Nowak. Random Kuhn-Tucker theorem. In Transactions of the ninth Prague conference on information theory, statistical decision functions, random processes, Vol. B (Prague, 1982), pages 95–97. Reidel, Dordrecht, 1983. [2799] Andrzej S. Nowak. Stationary equilibria for non-zero-sum average payoff ergodic stochastic games with general state space. In Advances in dynamic games and applications (Geneva, 1992), volume 1 of Ann. Internat. Soc. Dynam. Games, pages 231–246. Birkhauser¨ Boston, Boston, MA, 1994. [2800] Maciej Nowak. Aspiration level approach in stochastic MCDM problems. European J. Oper. Res., 177(3):1626–1640, 2007.

157 [2801] Matthias P. Nowak and Werner Romisch.¨ Stochastic Lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty. Ann. Oper. Res., 100:251–272 (2001), 2000. Research in stochastic programming (Vancouver, BC, 1998). [2802] Matthias P. Nowak, Rdiger Schultz, and Markus Westphalen. Optimization of simultaneous power production and trading by stochastic integer programming. Stochastic Programming E-Print Series, http://www.speps.org, 2002. [2803] Matthias P. Nowak, Rudiger¨ Schultz, and Markus Westphalen. A stochastic integer programming model for incorporating day-ahead trading of electricity into hydro-thermal unit commitment. Op- tim. Eng., 6(2):163–176, 2005. [2804] M.P. Nowak, R. Nurnberg,¨ W. Romisch,¨ R. Schultz, and M. Westphalen. Stochastic programming for power production and trading under uncertainty. Preprint SM-DU-471, Fachbereich Mathe- matik, Universitat¨ Duisburg, 2000. submitted. [2805] M.P. Nowak and W. Romisch.¨ Stochastic lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty. Annals of Operations Research, 100, 2001. to appear. [2806] Nilay Noyan, Gabor´ Rudolf, and Andrzej Ruszczynski.´ Relaxations of linear programming problems with ﬁrst order stochastic dominance constraints. Oper. Res. Lett., 34(6):653–659, 2006. [2807] Nilay Noyan and Andrzej Ruszczynski. Valid inequalities and restrictions for stochastic programming problems with ﬁrst order stochastic dominance constraints. Optimization Online, http://www.optimization-online.org, 2006.

[2808] Frantisekˇ Noziˇ cka.ˇ uber¨ einfache Mannigfaltigkeiten in linearem afﬁnen Raum An in globaler Auffassung. Czechoslovak Math. J., 26(101)(4):541–578, 1976. [2809] Lewis Ntaimo and Suvrajeet Sen. The million-variable ”march” for stochastic combinatorial optimization. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [2810] Lewis Ntaimo and Suvrajeet Sen. A comparative study of decomposition algorithms for stochastic combinatorial optimization. Stochastic Programming E-Print Series, http://www.speps. org, 2005. [2811] Lewis Ntaimo and Suvrajeet Sen. The million-variable “march” for stochastic combinatorial optimization. J. Global Optim., 32(3):385–400, 2005. [2812] Lewis Ntaimo and Suvrajeet Sen. A branch-and-cut algorithm for two-stage stochastic mixed- binary programs with continuous ﬁrst-stage variables. Stochastic Programming E-Print Series, http://www.speps.org, 2006. [2813] Lewis Ntaimo and Matthew W. Tanner. Computations with disjunctive cuts for two-stage stochastic mixed 0-1 integer programs. Stochastic Programming E-Print Series, http://www.speps. org, 2007. [2814] E.A. Nurminskii. Conditions for the convergence of stochastic programming algorithms. Kiber- netika (Kiev), 3:84–87, 1973. [2815] E.A. Nurminskii. Chislennye metody resheniya determinirovannykh i stokhasticheskikh minimaksnykh zadach. “Naukova Dumka”, Kiev, 1979. [2816] E.A. Nurminskij. Numerical methods of the solution of deterministic and stochastic minimax problems. (Chislennye metody resheniya determinirovannykh i stokhasticheskikh minimaksnykh zadach.). Akademiya Nauk Ukrainskoj SSR, Ordena Lenina Institut Kibernetiki. Kiev: ”Naukova Dumka”., 1979. [2817] E. M. Oblow. SPT: a stochastic tunneling algorithm for global optimization. J. Global Optim., 20(2):195–212, 2001.

158 [2818] Ralf Oestermark. A chance-constraint programming approach to the capital pricing model. Kyber- netes 20, No.5, 42-49, 1991. [2819] Wlodzimierz Ogryczak and Andrzej Ruszczynski.´ Dual stochastic dominance and related mean- risk models. SIAM J. Optim., 13(1):60–78 (electronic), 2002. [2820] James A. Ohlson. Quadratic approximations of the portfolio selection problem when the means and variances of returns are infinite. Management Sci. 23, 576-584, 1977. [2821] Yoshio Ohtsubo. Optimal control of the service rate and the stopping rule in an M/G/1 queue. Mem. Fac. Sci., Kochi Univ., Ser. A 3, 75-103, 1982. [2822] Sigurdur Olafsson.´ Two-stage nested partitions method for stochastic optimization. Methodol. Comput. Appl. Probab., 6(1):5–27, 2004. [2823] Sigurdur Olafsson´ and Leyuan Shi. Ordinal comparison via the nested partitions method. Discrete Event Dyn. Syst., 12(2):211–239, 2002. [2824] Niels J. Olieman and Bram van Putten. Estimation method of multivariate exponential probabilities based on a simplex coordinates transform. Stochastic Programming E-Print Series, http:// www.speps.org, 2006. [2825] G. C. Oliveira, M. V. F. Pereira, S. H. F. Cunha, and S. Granville. Multi-area capacity expansion model with reliability constraints. PSCC ’87, 1987. [2826] Paul Olsen. Polyhedral convex feasible regions in stochastic programming with recourse. In Pro- ceedings of the IEEE Conference on Decision and Control including the 14th Symposium on Adap- tive Processes (Houston, Tex., 1975), pages 593–597. Inst. Electr. Electron. Engrs., New York, 1975. [2827] Paul Olsen. Discretizations of multistage stochastic programming problems. Math. Programming Stud., 6:111–124, 1976. Stochastic systems: modeling, identification and optimization, II (Proc. Sympos., Univ. Kentucky, Lexington, Ky.,1975). [2828] Paul Olsen. Multistage stochastic programming with recourse as mathematical programming in an l p space. SIAM J. Control Optimization, 14(3):528–537, 1976. [2829] Paul Olsen. Multistage stochastic programming with recourse: the equivalent deterministic problem. SIAM J. Control Optimization, 14(3):495–517, 1976. [2830] Paul Olsen. When is a multistage stochastic programming problem well-defined? SIAM J. Control Optimization, 14(3):518–527, 1976. [2831] David L. Olson and Scott R. Swenseth. A linear approximation for chance-constrained programming. J. Oper. Res. Soc. 38, 261-267, 1987. [2832] A. Orden. A study of pivot probabilities in LP tableaus. In Survey of mathematical programming (Proc. Ninth Internat. Math. Programming Sympos., Budapest, 1976), Vol. 2, pages 141–154. North-Holland, Amsterdam, 1979. [2833] S.A. Orlovsky. On formalization of a general fuzzy mathematical problem. Fuzzy Sets and Systems, 3(3):311–321, 1980. [2834] P. M. Ortigosa, J. L. Redondo, I. García, and J. J. Fernandez.´ A population global optimization algorithm to solve the image alignment problem in electron crystallography. J. Global Optim., 37(4):527–539, 2007. [2835] Shunji Osaki, D.N.P. Murthy, and R.J. Wilson, editors. Stochastic models in engineering, technology and management. Pergamon Press, Exeter, 1995. Papers from the Australian-Japan Workshop held on the Gold Coast, July 14–16, 1994, Math. Comput. Modelling 22 (1995), no. 10-12.

159 [2836] M.R. Osborne. A finite algorithm for the rank regression problem. In Essays in statistical science, Pap. in Honour of P.A.P. Moran, J. Appl. Probab., Spec. Vol. 19A, 241-252, 1982. [2837] M.R. Osborne and G.A. Watson. An analysis of the total approximation problem in separable norms, and an algorithm for the total l1 problem. SIAM J. Sci. Statist. Comput., 6(2):410–424, 1985. [2838] Ju.S. Osipov. On the theory of differential games in distributed parameter systems. Sov. Math., Dokl. 16, 1093-1097 translation from Dokl. Akad. Nauk SSSR 223, 1314-1317 (1975)., 1975. [2839] John Otto, Marius Paraschivoiu, Serhat Yes¸ilyurt, and Anthony T. Patera. Bayesian-validated computer-simulation surrogates for optimization and design: error estimates and applications. Math. Comput. Simulation, 44(4):347–367, 1997. IMACS-COST Conference on Computational Fluid Dynamics, Three-dimensional Complex Flows (Lausanne, 1995). [2840] Hiroyuki Ozaki and Peter A. Streufert. Dynamic programming for non-additive stochastic objectives. J. Math. Econom., 25(4):391–442, 1996. [2841] Mufit Ozden and Yu-Chi Ho. A probabilistic solution-generator for simulation. European J. Oper. Res., 146(1):35–51, 2003. [2842] Tae Je Pak. Study about statistical properties of extremum estimators in a method on global random search. Su-hak, 1:14–19, 1988. [2843] Udatta S. Palekar, Rajan Batta, Robert M. Bosch, and Sharad Elhence. Modeling uncertainties in plant layout problems. Eur. J. Oper. Res. 63, No.2, 347-359, 1992. [2844] F. Pan, W. Charlton, and D.P. Morton. Interdicting smuggled nuclear material. In D.L. Woodruff, editor, Network Interdiction and Stochastic Integer Programming, pages 1–20. Kluwer Academic Publishers, Boston, 2003. [2845] Rufang Pan. A simple solution for fuzzy linear programming. Nat. Sci. J. Xiangtan Univ. 1987, No.3, 29-36, 1987. [2846] J.-C. Panayiotopoulos. The multidimensional assignment model with provision for an uncertain future. J. Inform. Optim. Sci., 1(1):94–101, 1980. [2847] G. Panda, D.A. Khan, and U.C. Ray. A jels stochastic inventory model with random demand. Stochastic Programming E-Print Series, http://www.speps.org, 2006. [2848] Jong-Shi Pang. A parametric linear complementarity technique for optimal portfolio selection with a risk-free asset. Oper. Res. 28, 927-941, 1980. [2849] Christos H. Papadimitriou. Games against nature. J. Comput. System Sci., 31(2):288–301, 1985. Special issue: Twenty-fourth annual symposium on the foundations of computer science (Tucson, Ariz., 1983). [2850] Nikolaos S. Papageorgiou. Stochastic nonsmooth analysis and optimization in Banach spaces. In Infinite programming (Cambridge, 1984), volume 259 of Lecture Notes in Econom. and Math. Systems, pages 226–242, Berlin, 1985. Springer. [2851] G.P. Papavassilopoulos. On the probability of existence of pure equilibria in matrix games. J. Optim. Theory Appl., 87(2):419–439, 1995. [2852] G.P. Papavassilopoulos. Addendum: “On the probability of existence of pure equilibria in matrix games” [J. Optim. Theory Appl. 87 (1995), no. 2, 419–439; MR 96h:90149]. J. Optim. Theory Appl., 91(3):729–730, 1996. [2853] Ju.M. Paramonov. Bestimmung der festzusetzenden Ressource bei einer kleinen Zahl von vorherge- henden Beobachtungen. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1975, Nr. 5, 120-123, 1975.

160 [2854] P.M. Pardalos and K.G. Ramakrishnan. On the expected optimal value of random assignment problems: experimental results and open questions. Comput. Optim. Appl., 2(3):261–271, 1993. [2855] E. Parent and F. Lebdi. Bicriterion operation of a water resources system with reliability-based tradeoffs. Appl. Math. Comput. 54, No.2-3, 197-213, 1993. [2856] S.R. Parimi and M.Z. Cohn. Optimal criteria in probabilistic structural design. In Optim. struct. Des., IUTAM-Symp. Warsaw 1973, 278-293, 1975. [2857] Mahmut Parlar. Stochastic control of a pension fund model with first-order Markov-dependent parameters. Optimal Control Appl. Methods, 2(2):175–189, 1981. [2858] Mahmut Parlar. A stochastic production planning model with a dynamic chance constraint. Eur. J. Oper. Res. 20, 255-260, 1985. [2859] Panos Parpas and BerçRustem. Computational assessment of nested benders and augmented La- grangian decomposition for mean-variance multistage stochastic problems. INFORMS J. Comput., 19(2):239–247, 2007. [2860] Panos Parpas, BerçRustem, and Efstratios N. Pistikopoulos. Linearly constrained global optimization and stochastic differential equations. J. Global Optim., 36(2):191–217, 2006. [2861] Robert Parviainen. Random assignment with integer costs. Combin. Probab. Comput., 13(1):103– 113, 2004. [2862] S.V. Pashko. On the convergence rate of the stochastic linearization method. Kibernetika 1984, No.4, 118-119, 1984. [2863] S.V. Pashko. The rate of convergence of the stochastic linearization method. Issled. Operatsii i ASU, 23:9–13, 138, 1984. [2864] S.V. Pashko. Optimality of the subgradient method for solving problems of stochastic programming. Dokl. Akad. Nauk Ukrain. SSR Ser. A, 8:76–79, 88, 1986. [2865] S.V. Pashko. The complexity of strongly convex problems of stochastic programming. Kibernetika (Kiev), 2:118–121, 135, 1987. [2866] E. L. Pasiliao. Transient stochastic models for search patterns. In Stochastic optimization: algorithms and applications (Gainesville, FL, 2000), volume 54 of Appl. Optim., pages 265–277. Kluwer Acad. Publ., Dordrecht, 2001. [2867] Jesus´ T. Pastor, Jose´ L. Ruiz, and Inmaculada Sirvent. A statistical test for nested radial DEA models. Oper. Res., 50(4):728–735, 2002. [2868] Nitin R. Patel. On wait-and-see stochastic linear programmes: an application and an algorithm. J. Oper. Res. Soc., 31(8):733–741, 1980. [2869] Vivek Patkar, P.C. Saxena, and Om Parkash. Dual program for a convex fractional function. Econom. Comput. Econom. Cybernet. Stud. Res., 15(1):77–80, 1981. [2870] Michael Patriksson and Laura Wynter. Stochastic mathematical programs with equilibrium constraints. Oper. Res. Lett., 25(4):159–167, 1999. [2871] Michele` Pavon and Roger J.-B. Wets. The duality between estimation and control from a variational viewpoint: the discrete time case. Math. Programming Stud., 18:1–11, 1982. Algorithms and theory in filtering and control (Lexington, Ky., 1980). [2872] Mieczyslaw Pazdur and Anna Pazdur. Application of the nonlinear least squares method to the estimation of the parameters of a function for approximation of the results of measurements. Zeszyty Nauk. Politech. Slk´ ask. Mat.-Fiz., 32:101–109, 1980.

161 [2873] Martin Pelikan, David E. Goldberg, and Fernando G. Lobo. A survey of optimization by building and using probabilistic models. Comput. Optim. Appl., 21(1):5–20, 2002. [2874] Martin Pelikan, Kumara Sastry, and David E. Goldberg. Scalablity of the Bayesian optimization algorithm. Internat. J. Approx. Reason., 31(3):221–258, 2002. Synergies between evolutionary computation and probabilistic graphical models. [2875] Rainer Pelizaeus. Konvexitaetsaussagen beim stochastischen linearen Programmieren mit Wahrscheinlichkeitsrestriktionen. Oper. Res. Verfahren 30, 130-153, 1979. [2876] Rainer Pelizaeus. Der Rand des zulaessigen Bereichs beim stochastischen linearen Optimieren mit Wahrscheinlichkeitsrestriktionen. Methods Oper. Res. 47, 85-94, 1983. [2877] Rainer Pelizaeus. Konvexitaetsaussagen beim stochastischen linearen Programmieren. Zwei Beispiele zur Berechnung alpha-extremaler Punkte. Methods Oper. Res. 47, 95-106, 1983. [2878] Rainer Pelizaeus. Korrespondenzen und Wahrscheinlichkeitsrestriktionen beim stochastischen linearen Optimieren. Methods Oper. Res. 47, 75-84, 1983. [2879] Jian-ping Peng and Ding-hua Shi. Improvement of pure random search in global optimization. J. Shanghai Univ., 4(2):92–95, 2000. [2880] Jin Peng and Baoding Liu. A framework of birandom theory and optimization methods. Informa- tion, 9(4):629–640, 2006. [2881] Teemu Pennanen. Epi-convergent discretizations of multistage stochastic programs. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [2882] Teemu Pennanen. Epi-convergent discretizations of multistage stochastic programs via integration quadratures. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [2883] Teemu Pennanen. Epi-convergent discretizations of multistage stochastic programs. Math. Oper. Res., 30(1):245–256, 2005. [2884] Teemu Pennanen and Markku Kallio. A splitting method for stochastic programs. Ann. Oper. Res., 142:259–268, 2006. [2885] Teemu Pennanen and Alan J. King. Arbitrage pricing of american contingent claims in incomplete markets - a convex optimization approach. Stochastic Programming E-Print Series, http:// www.speps.org, 2004. [2886] Teemu Pennanen and Matti Koivu. Integration quadratures in discretization of stochastic programs. Stochastic Programming E-Print Series, http://www.speps.org, 2002. [2887] Teemu Pennanen and Matti Koivu. Epi-convergent discretizations of stochastic programs via integration quadratures. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [2888] Teemu Pennanen and Matti Koivu. Epi-convergent discretizations of stochastic programs via integration quadratures. Numer. Math., 100(1):141–163, 2005. [2889] Allon G. Percus and Olivier C. Martin. The stochastic traveling salesman problem: ﬁnite size scaling and the cavity prediction. J. Statist. Phys., 94(5-6):739–758, 1999. [2890] M. V. F. Pereira, N. M. Campodonico,´ B. G. Gorenstin, and J. P. Costa. Application of stochastic optimization to power system planning and operation. In Proceedings of the IEEE Stockholm Power Tech, pages 234–239, Stockholm, Sweden, 1995. [2891] M. V. F. Pereira and L. M. V. G Pinto. Stochastic optimization of a multireservoir hydroelectric system—a decomposition approach. Water Resources Research, 21(6):779–792, 1985.

162 [2892] M.V.F. Pereira and L.M.V.G. Pinto. Multi-stage stochastic optimization applied to energy planning. Math. Programming, 52(2, Ser. B):359–375, 1991. [2893] I.I. Perel’man. Stationary adaptive search strategy as an alternative to the method of stochastic approximation. Autom. Remote Control 48, No.11, 1517-1527 translation from Avtom. Telemekh. 1987, No.11, 132-143 (1987)., 1987. [2894] A.G. Perevozchikov. A method for the approximation of the pseudogradient mapping of the function of the connected maximum. Zh. Vychisl. Mat. i Mat. Fiz., 31(3):353–362, 1991. [2895] A.G. Perevozchikov. On the approximation of generalized stochastic gradients of random regular functions. Zh. Vychisl. Mat. i Mat. Fiz., 31(5):681–688, 1991. [2896] A.G. Perevozchikov. The stochastic method of generalized Clarke gradients for solving two- stage problems of stochastic programming with coupled variables. Comput. Math. Math. Phys. 33, No.3, 411-414 translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No.3, 453-455 (1993)., 1993. [2897] G. Perez-Lechuga,´ M. M. Alvarez-Su´ arez,´ J. Garnica-Gonzalez,´ H. Niccolas-Morales, and F. Venegas-Mart´inez. Stochastic linear programming to optimize some stochastic systems. WSEAS Trans. Syst., 5(9):2263–2268, 2006. [2898] C. Perkgoz, K. Kato, H. Katagiri, and M. Sakawa. An interactive fuzzy satisﬁcing method for multiobjective stochastic integer programming problems through variance minimization model. Sci. Math. Jpn., 60(2):327–336, 2004. [2899] Cary D. Perttunen. A nonparametric global optimization method using the rank transformation. In Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1–3 (Tampa, FL, 1989), pages 888–893, New York, 1989. IEEE. [2900] Cary D. Perttunen and Bruce E. Stuckman. The normal score transformation applied to a multi- univariate method of global optimization. J. Global Optim., 2(2):167–176, 1992. [2901] Anatoli A. Pervozvanski and Vladimir G. Gajcgori. Operative control of industrial activity as a problem of stochastic programming. Systems Sci., 3(1):91–95, 1977. [2902] A.A. Pervozvanskij and V.G. Gajtsgori. Decomposition, aggregation and approximate optimization. (Dekompozitsiya, agregirovanie i priblizhennaya optimizatsiya). Teoriya i Metody Sis- temnogo Analiza. Moskva: ”Nauka”., 1979. [2903] Robert J. Peters, Klaas Boskma, and Hendrik A.E. Kupper. Stochastic programming in production planning: A case with none-simple recourse. Statistica Neerlandica 31, 113-126, 1977. [2904] Robert J. Peters, Kai-Ching Chu, and Mohammad Jamshidi. Optimal operation of a water resources system by stochastic programming. In Math. Progr. in Use, Math. Progr. Study 9, 152-175, 1978. [2905] I. Petersen. Reduction of risk using a differentiated approach. In Stochastic optimization, Proc. Int. Conf., Kiev/USSR 1984, Lect. Notes Control Inf. Sci. 81, 496-500, 1986. [2906] L. Petersen. Stochastic optimization by smoothing. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1969, No.2, 36-44, 1969. [2907] Dobia´sˇ Petr. Contamination technigue for two-stage stochastic integer programs. In Proceedings of 18th International Conference; Mathematical Methods in Economics, pages 33–38, 2000. [2908] V.V. Petrov, V.M. Ageev, A.V. Zaporozec,ˇ A.V. Kort’ev, V.M. Kostjukov, S.B. Medvedev, and I.N. Poljakov. Information theory of complex systems functioning under conditions of incomplete information. In Engineering cybernetics, Vol. 13 (Russian), pages 121–151. Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1980.

163 [2909] U. Pferschy. The random linear bottleneck assignment problem. RAIRO Rech. Oper.´ , 30(2):127– 142, 1996. [2910] G. Ch. Pflug. Stepsize rules, stopping times and their implementation in stochastic quasigradient algorithms. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 353–372. Springer, Berlin, 1988. [2911] G. Ch. Pflug, A. Swie¸tanowski,´ E. Dockner, and H. Moritsch. The Aurora financial management system: model and parallel implementation design. Ann. Oper Res., 99:189–206 (2001), 2000. Applied mathematical programming and modeling, IV (Limassol, 1998). [2912] G.Ch. Pflug. On the penalization method in convex stochastic programming. In Operations research in progress, Theory Decis. Libr. 32, 49-55, 1982. [2913] G.Ch. Pflug. On-line optimization of simulated Markovian processes. Math. Oper. Res. 15, No.3, 381-395, 1990. [2914] G.Ch. Pflug and A. Ruszczynski,´ editors. Thirteenth EURO Summer Institute: Stochastic Opti- mization. North-Holland, Amsterdam, 1997. EJOR 101, No. 2. [2915] Georg Ch. Pflug. On the convergence of a penalty-type stochastic optimization procedure. J. Inform. Optim. Sci., 2(3):249–258, 1981. [2916] Georg Ch. Pflug. Stochastic minimization with constant step-size: Asymptotic laws. SIAM J. Control Optimization 24, 655-666, 1986. [2917] Georg Ch. Pflug. Derivatives of probability measures - concepts and applications to the optimization of stochastic systems. In Discrete event systems: models and applications, IIASA Conf., Sopron/Hung. 1987, Lect. Notes Control Inf. 103, 252-274, 1988. [2918] Georg Ch. Pflug. Asymptotic stochastic programs. Math. Oper. Res., 20(4):769–789, 1995. [2919] Georg Ch. Pflug. Optimization of stochastic models. Kluwer Academic Publishers, Boston, MA, 1996. The interface between simulation and optimization. [2920] Georg Ch. Pflug. Stochastic programs and statistical data. Ann. Oper. Res., 85:59–78, 1999. Stochastic programming. State of the art, 1998 (Vancouver, BC). [2921] Georg Ch. Pflug and Andrzej Ruszczynski.´ Risk measures for income streams. Stochastic Pro- gramming E-Print Series, http://www.speps.org, 2001. [2922] Georg Ch. Pflug, Andrzej Ruszczynski,´ and Rudiger¨ Schultz. On the Glivenko-Cantelli problem in stochastic programming: linear recourse and extensions. Math. Oper. Res., 23(1):204–220, 1998. [2923] Georg Ch. Pflug, Andrzej Ruszczynski,´ and Rudiger¨ Schultz. On the Glivenko-Cantelli problem in stochastic programming: mixed-integer linear recourse. Math. Methods Oper. Res., 47(1):39–49, 1998. [2924] Georg Ch. Pflug and Heinz Weisshaupt. Probability gradient estimation by set-valued calculus and applications in network design. SIAM J. Optim., 15(3):898–914 (electronic), 2005. [2925] Huyenˆ Pham. On quadratic hedging in continuous time. Math. Methods Oper. Res., 51(2):315–339, 2000. [2926] V.C. Phan. Quelques theor´ emes` de point fixe pour des multifonctions aleatoires´ de type de contraction. Travaux Sem.´ Anal. Convexe, 10(1):exp. no. 7, 27, 1980. [2927] C. R. Philbrick and P. K. Kitanidis. Limitations of deterministic optimization applied to reservoir operations. Journal of Water Resources Planning and Management-ASCE, 125(3):135–142, 1999.

164 [2928] A.T. Phillips, J.B. Rosen, and M. van Vliet. A parallel stochastic method for solving linearly constrained concave global minimization problems. J. Global Optim., 2(3):243–258, 1992. Conference on Computational Methods in Global Optimization, II (Princeton, NJ, 1991). [2929] A. B. Philpott. Stochastic optimization and yacht racing. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 315–336. SIAM, Philadelphia, PA, 2005. [2930] A. B. Philpott, M. Craddock, and H. Waterer. Hydro-electric unit commitment subject to uncertain demand. European Journal of Operational Research, 125(2):410–424, 2000. [2931] Andy Philpott and Geoff Leyland. Rowing to Barbados. In S. Albers, R.H. Mohring,¨ G.Ch. Pﬂug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [2932] Nguyen Van Pho. On a mathematical model of the optimal reliability theory and some mechanical applications. Teor. Prilozhna Mekh. 1986, No.2, 100-106, 1986. [2933] Mustafa C¸. Pi nar. Robust scenario optimization based on downside-risk measure for multi-period portfolio selection. OR Spectrum, 29(2):295–309, 2007. [2934] James B. Pickens, John G. Hof, and Brian M. Kent. Use of chance-constrained programming to account for stochastic variation in the A-matrix of large-scale linear programs: a forestry application. Ann. Oper. Res., 31(1-4):511–526, 1991. Stochastic programming, Part II (Ann Arbor, MI, 1989). [2935] Nanda Piersma. A probabilistic analysis of the capacitated facility location problem. J. Comb. Optim., 3(1):31–50, 1999.

[2936] Francisco A. Pino and Pedro A. Morettin. The consistency of the L1-norm estimates in ARMA models. Comm. Statist. Theory Methods, 22(8):2185–2206, 1993. [2937] J. Pinter. Hybrid procedures for solving non-smooth stochastic problems of constrained minimization. Vestn. Mosk. Univ., Ser. XV 1982, No.1, 39-49, 1982. [2938] J. Pinter. Mixed procedures for the solution of nonsmooth stochastic conditional minimization problems. Mosc. Univ. Comput. Math. Cybern. 1982, No.1, 47-57, 1982. [2939] J. Pinter.´ Stochastic optimization methods for solving mathematical programming problems. In Statistics and probability (Visegrad,´ 1982), pages 271–282. Reidel, Dordrecht, 1984. [2940] J. Pinter.´ Deterministic approximations of probability inequalities. Z. Oper. Res., 33(4):219–239, 1989. [2941] Janos Pinter. A stochastic programming model, applied to water resources management. Budapest: Computung Center for Universities., 1975. [2942] Janos´ Pinter.´ Evaluation of a stochastic gradient optimization algorithm, volume 23 of ESZK. Computing Center for Universities Department of Applied Mathematics, Budapest, 1978. With Hungarian and Russian summaries. [2943] Janos´ Pinter.´ On the convergence and numerical effectiveness of random search procedures. Alka- lmaz. Mat. Lapok, 4(3-4):197–228 (1979), 1978. [2944] Janos Pinter. On a stochastic model of reservoir system sizing. In Optimization techniques, Proc. 9th IFIP Conf., Warsaw 1979, Part 2, Lect. Notes Control Inf. Sci. 23, 546-558, 1980. [2945] Janos´ Pinter.´ Hybrid optimization procedures for the solution of nonsmooth stochastic problems. Alkalmaz. Mat. Lapok, 7(1-2):83–97, 1981.

165 [2946] Janos´ Pinter.´ Stochastic procedures for solving optimization problems. Alkalmaz. Mat. Lapok, 7(3-4):217–252, 1981. [2947] Janos Pinter. Stochastically combined optimization procedures, their convergence and numerical performance. Methods Oper. Res. 43, 143-150, 1981. [2948] Janos´ Pinter.´ Convergence properties of stochastic optimization procedures. Math. Operations- forsch. Statist. Ser. Optim., 15(3):405–427, 1984. [2949] Janos´ Pinter.´ Contributions to the methodology of stochastic optimization. In Stochastic programming (Gargnano, 1983), volume 76 of Lecture Notes in Control and Inform. Sci., pages 247–257. Springer, Berlin, 1986. [2950] Janos Pinter. Stochastic modelling and optimization for environmental management. Ann. Oper. Res. 31, 527-544, 1991. [2951] J.D. Pinter. On the maximal distance between two series of empirical distribution functions, with application to an inventory problem. Methods of Operations Research, 29:623–636, 1978. [2952] J.D. Pinter. A modiﬁed Bernstein-technique for estimating noise-perturbed function values. Cal- colo, 22:241–247, 1985. [2953] J.D. Pinter. Stochastic decision models for RA&M (risk analysis and management): A brief methodological overview. Research Report 90.068, National Institute for Inland Water Manage- ment and Waste Water Treatment, Lelystad, 1990. [2954] J.D. Pinter. Global Optimization in Action. Kluwer Academic Publishers, Dordrecht / Boston / London, 1996. [2955] J.D. Pinter. A model development system for global optimization. In R. De Leone, A. Murli, P.M. Pardalos, and G. Toraldo, editors, High Performance Software for Nonlinear Optimizaton: Status and Perspectives, pages 301–314. Kluwer Academic Publishers, Dordrecht / Boston / London, 1998. [2956] J.D. Pinter. LGO - A Model Development System for Continuous Global Optimization. User’s Guide. Pinter Consulting Services, Inc., Halifax, NS, Canada, 1999. [2957] J.D. Pinter and L. Somlyody. A stochastic lake eutrophication management model. In V.I. Arkin, A.N. Shiriaev, and R. Wets, editors, Stochastic Optimization (Kiev, Sept. 1984). Lecture Notes in Control and Information Sciences 81, pages 501–512, Berlin Heidelberg New York, 1986. Springer-Verlag. [2958] J.D. Pinter and D.T. van der Molen. Environmental model calibration under different problem speciﬁcations: An application to the model SED. Ecological Modelling, 68:1–19, 1993. [2959] Zdenek Piras. Use of stochastic programming for the design of elastic-plastic one dimensional systems. Acta techn. CSAV 17, 667-694, 1972. [2960] F.M. Pires and J.J. Judice.´ Direct methods for convex quadratic problems with restrictions only on the values of the variables. In Proceedings of the XIIth Portuguese-Spanish Conference on Mathematics, Vol. III (Portuguese) (Braga, 1987), pages 289–296, Braga, 1987. Univ. Minho. [2961] O. Pirohanic. Suboptimal stochastic control strategy and an alternative cost decomposition. Int. J. Control 44, 1297-1318, 1986. [2962] A.B. Piunovskii. Control of impulsive processes in problems with constraints. Avtomat. i Tele- mekh., 4:75–89, 1994.

166 [2963] Luis M. Pla, Josep Conde, and Jesus´ Pomar. Stochastic dynamic programming the sow replacement problem. In Proceedings of the 3rd Catalan Days on Applied Mathematics (Lleida, 1996), pages 175–184. Univ. Lleida, Lleida, 199? [2964] V. P. Plagianakos, G. D. Magoulas, and M. N. Vrahatis. Learning rate adaptation in stochastic gradient descent. In Advances in convex analysis and global optimization (Pythagorion, 2000), volume 54 of Nonconvex Optim. Appl., pages 433–444. Kluwer Acad. Publ., Dordrecht, 2001. [2965] E.L. Plambeck, B.-R. Fu, S.M. Robinson, and R. Suri. Throughput optimization in tandem production lines via nonsmooth programming. In J. Schoen, editor, Proceedings of 1993 Summer Computer Simulation Conference, pages 70–75, San Diego, CA, 1993. Society for Computer Sim- ulation. [2966] Erica L. Plambeck, Bor-Ruey Fu, Stephen M. Robinson, and Rajan Suri. Sample-path optimization of convex stochastic performance functions. Math. Programming, 75(2, Ser. B):137–176, 1996. Approximation and computation in stochastic programming. [2967] Stanley R. Pliska. Duality theory for some stochastic control models. In Stochastic differential systems, Proc. 2nd Conf., Bad Honnef 1982, Lect. Notes Control Inf. Sci. 43, 329-337, 1982. [2968] Ernst Ploechinger. Limit theorems on the Robbins-Monro process for different variance behaviors of the stochastic gradient. In Stochastic optimization. Numerical methods and technical applications, Proc. GAMM/IFIP-Workshop, Neubiberg/Ger. 1990, Lect. Notes Econ. Math. Syst. 379, 27-80, 1992. [2969] Ernst Ploechinger. Realisierung von adaptiven Schrittweiten fuer stochastische Approxima- tionsverfahren bei unterschiedlichem Varianzverhalten des Schaetzfehlers. (Realization of adaptive step widths for stochastic approximation methods at different behaviour of the variance of the estimation processor)., 1992. [2970] Frederick van der Ploeg. A closed-form solution for a model of precautionary saving. Rev. Econ. Stud. 60, No.2, 385-395, 1993. [2971] V.V. Podinovskii. Lexikographische Optimierungsprobleme unter Unbestimmtheitsbedingungen. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1973, Nr. 1, 32-37, 1972. [2972] V.V. Podinovskii. Ueber die Loesung multikriterialer Probleme als monokriteriale Opti- mierungsprobleme unter Unbestimmtheit. Avtomatika vycislit. Tehn., Riga 1976, Nr. 2, 45-49, 1976. [2973] V.V. Podinovskiy. Lexicographical problems of optimization under conditions of indeterminacy. Engrg. Cybernetics, 11(1):28–33, 1973. [2974] J. Poepplau. Die Anwendung einer (mu/rho,lambda)-Evolutionsstrategie zur direkten Minimierung eines nichtlinearen Funktionals unter Verwendung von FE- Ansatzfunktionen am Beispiel des Brachistochronenprolbems. Z. Angew. Math. Mech. 61, T 305-T 307, 1981. [2975] V. Pogozel’ski.ˇ An application of a certain classification procedure to the improvement of a search for the global minimum. In Problems of random search, 2 (Russian), pages 127–130, 221. Izdat. “Zinatne”, Riga, 1973. [2976] V. Pogozel’ski.ˇ Determination of the best sequence for testing the fulfillment of constraints when using a statistical algorithm. In Problems of random search, 2 (Russian), pages 151–156, 221. Izdat. “Zinatne”, Riga, 1973. [2977] M. Pogu and J.E. Souza de Cursi. Global optimization by random perturbation of the gradient method with a fixed parameter. J. Global Optim., 5(2):159–180, 1994.

167 [2978] Elijah Polak, Roger J.-B. Wets, and Armen der Kiureghian. On an approach to optimization problems with a probabilistic cost and or constraints. In Nonlinear optimization and related topics (Erice, 1998), pages 299–315. Kluwer Acad. Publ., Dordrecht, 2000. [2979] B.T. Poljak. Minimization of complex regression functions. Kibernetika (Kiev), 4:148–149, 1978. [2980] B.T. Poljak. Nonlinear programming methods in the presence of noise. In Survey of mathematical programming (Proc. Ninth Internat. Math. Programming Sympos., Budapest, 1976), Vol. 2, pages 155–165, Amsterdam, 1979. North-Holland. [2981] B.T. Poljak and Ya. Z. Tsypkin. Optimal and robust methods for unconditional optimization. In Control science and technology for the progress of society, Vol. 1 (Kyoto, 1981), pages 519–523. IFAC, Laxenburg, 1982. [2982] M.A. Pollatschek. Bounds for stochastic convex programs. Z. Operations Res. Ser. A-B, 18:A27– A39, 1974. [2983] B. T. Polyak. Robust stability of interval matrices: a stochastic approach. In Stochastic programming methods and technical applications (Neubiberg/Munich, 1996), pages 202–207. Springer, Berlin, 1998. [2984] B. T. Polyak. Random algorithms for solving convex inequalities. In Inherently parallel algorithms in feasibility and optimization and their applications (Haifa, 2000), volume 8 of Stud. Comput. Math., pages 409–422. North-Holland, Amsterdam, 2001. [2985] B. T. Polyak and Ya. Z. Tsypkin. Optimal and robust methods for stochastic optimization. Nova J. Math. Game Theory Algebra, 6(2-3):163–176, 1997. [2986] B.T. Polyak. Methods for solving constrained extremum problems in the presence of random noise. U.S.S.R. Comput. Math. Math. Phys. 19, No.1, 72-81 translation from Zh. Vychisl. Mat. Mat. Fiz. 19, 70-78 (1979)., 1980. [2987] B.T. Polyak. A new method of stochastic approximation type. Avtomat. i Telemekh., 7:98–107, 1990. [2988] B.T. Polyak and A.B. Tsybakov. Optimal order of accuracy of search algorithms in stochastic optimization. Probl. Inf. Transm. 26, No.2, 126-133 translation from Probl. Peredachi Inf. 26, No.2, 45-53 (1990)., 1990. [2989] B.T. Polyak and Ya. Z. Tsypkin. Optimal pseudogradient adaptation algorithms. Automat. Remote Control, 41(8, part 1):1101–1110 (1981), 1980. [2990] B.T. Polyak and Ya. Z. Tsypkin. Optimal algorithms for criterial optimization under conditions of uncertainty. Dokl. Akad. Nauk SSSR, 273(2):315–318, 1983. [2991] B.T. Polyak and Ya.Z. Tsypkin. Optimal pseudogradient stochastic-optimization algorithms. Sov. Phys., Dokl. 25, 85-87 translation from Dokl. Akad. Nauk SSSR 250, 1084-1087 (1980)., 1980. [2992] B.T. Polyak and Ya.Z. Tsypkin. Criterion algorithms of stochastic optimization. Autom. Remote Control 45, 766-774 translation from Avtom. Telemekh. 1984, No.6, 95-104 (1984)., 1984. [2993] George H. Polychronopoulos and John N. Tsitsiklis. Stochastic shortest path problems with recourse. Networks, 27(2):133–143, 1996. [2994] Andreas Ponn. Optimale Zentrierung von Produktionsprozessen. (Optimal centering of production processes)., 1989. [2995] Chandra A. Poojari, Cormac Lucas, and Gautam Mitra. Robust solution and risk measures for a supply chain planning problem under uncertainty. Stochastic Programming E-Print Series, http: //www.speps.org, 2006.

168 [2996] Chandra A. Poojari and Boby Varghese. Genetic algorithm based technique for solving chance constrained problems. Stochastic Programming E-Print Series, http://www.speps.org, 2006. [2997] Pavel Popela. Stochastic programming models and methods for technical applications. In Summer School DATASTAT 01, Proceedings (Cihˇ ak´ Cottage), volume 11 of Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math., pages 181–206, Brno, 2002. Masaryk Univ. [2998] Ioana Popescu. Robust mean-covariance solutions for stochastic optimization. Oper. Res., 55(1):98–112, 2007. [2999] E. Popova and D. Morton. Adaptive stochastic manpower scheduling. In Proceedings of the Winter Simulation Conference, pages 661–668, 1998. [3000] I. Popova, D. P. Morton, E. Popova, and J. Yau. Optimizing benchmark-based portfolios with hedge funds. The Journal of Alternative Investments, 10:35–55, 2007. [3001] S.M. Porockii. Stochastische Zweietappenprobleme vom Transporttyp. Izv. Akad. Nauk SSSR, Tekh. Kibernet. 1977, No.2, 23-31, 1977. [3002] Z. Porosinski´ and K. Szajowski. Random priority two-person full-information best choice problem with imperfect observation. Appl. Math. (Warsaw), 27(3):251–263, 2000. [3003] S.M. Porotskiy. Two-step stochastic problems of the transport type. Engrg. Cybernet., 15(2):20–29 (1978), 1977. [3004] Evan L. Porteus. An adjustment to the Norman-White approach to approximating dynamic programs. Oper. Res. 27, 1203-1207, 1979. [3005] Dominique Potier. Algorithmes de coordination. Application a la gestion d’unites de production interdependantes. IRIA, Cahier 11, 241-387, 1972. [3006] B. Pourbabai. A heuristic algorithm for a stochastic transportation network. Optimization, 25(1):91–95, 1992. [3007] B. Pourbabai. An optimal policy for controlling the ﬂow time in an assembly line system. Opti- mization, 30(2):177–189, 1994. [3008] Behnam Pourbabai. A class of chance constrained network optimization problems. Appl. Math. Lett. 3, No.3, 91-94, 1990. [3009] Behnam Pourbabai. Minimum required local storages of an automated assembly system. J. Oper. Res. Soc. 43, No.2, 95-109, 1992. [3010] Behnam Pourbabai. An operational strategy for throughput maximization and bottleneck control in an assembly line system: By selection of the processing rates. J. Oper. Res. Soc. 44, No.10, 1003-1011, 1993. [3011] Warren Powell, Andrzej Ruszczynski, and Huseyin Topaloglu. Learning algorithms for separable approximations of stochastic optimization problems. Stochastic Programming E-Print Series, http://www.speps.org, 2002. [3012] Warren Powell, Andrzej Ruszczynski,´ and Huseyin Topaloglu. Learning algorithms for separable approximations of discrete stochastic optimization problems. Math. Oper. Res., 29(4):814–836, 2004. [3013] Warren B. Powell. A comparative review of alternative algorithms for the dynamic vehicle allocation problem. In Vehicle routing: Methods and studies, Stud. Manage. Sci. Syst. 16, 249-291 , 1988.

169 [3014] Warren B. Powell and Raymond K. Cheung. Stochastic programs over trees with random arc capacities. Networks, 24(3):161–175, 1994. [3015] Warren B. Powell and Huseyin Topaloglu. Fleet management. In Applications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 185–215. SIAM, Philadelphia, PA, 2005. [3016] A.S. Poznjak. Use of learning automata for the control of random search. Autom. Remote Control 33, 1992-2000 translation from Avtom. Telemekh. 1972, No.12, 88-97 (1972)., 1972. [3017] A.S. Poznjak. Learning automata in stochastic programming problems. Autom. Remote Control 34, 1608-1619 translation from Avtom. Telemekh. 1973, No.10, 84-96 (1973)., 1973. [3018] A. S. Poznyak and K. Najim. Learning automata and stochastic optimization. Springer-Verlag London Ltd., London, 1997. [3019] A.S. Poznyak. Recursive stochastic gradient procedures in the presence of dependent noise. In Stochastic optimization (Kiev, 1984), volume 81 of Lecture Notes in Control and Inform. Sci., pages 522–533. Springer, Berlin, 1986. [3020] A.S. Poznyak and Ya.Z. Tsypkin. Class-wise optimal algorithms for optimization in correlated- noise conditions. U.S.S.R. Comput. Math. Math. Phys. 24, 112-122, 1984. [3021] A.S. Poznyak and Ya.Z. Tsypkin. Optimization algorithms optimal on a class involving correlated noise. Zh. Vychisl. Mat. Mat. Fiz. 24, No.6, 806-822, 1984. [3022] L. Praly. Towards a direct adaptive control scheme for general disturbed MIMO systems. In Analysis and optimization of systems, Proc. 5th int. Conf., Versailles 1982, Lect. Notes Control Inf. Sci. 44, 353-366, 1982. [3023] A. Prekopa.´ On probabilistic constrained programming. In Proceedings of the Princeton Sym- posium on Mathematical Programming (Princeton Univ., 1967), pages 113–138, Princeton, N.J., 1970. Princeton Univ. Press. [3024] A. Prekopa.´ On the number of vertices of random convex polyhedra. Period. Math. Hungar., 2:259–282, 1972. Collection of articles dedicated to the memory of Alfred´ Renyi,´ I. [3025] A. Prekopa. Ein stochastisches dynamisches Programmierungsmodell. In 18. internat. wiss. Kol- loqu., Ilmenau 1 , 49-50, 1973. [3026] A. Prekopa.´ Optimal control of a storage level using stochastic programming. Problems of Control and Information Theory/Problemy Upravlenija i Teorii Informacii, 4(3):193–204, 1975. [3027] A. Prekopa.´ Dynamic type stochastic programming models. In Studies on mathematical programming (Papers, Third Conf. Math. Programming, Matraf´ ured,¨ 1975), volume 1 of Math. Methods Oper. Res., pages 127–145, Budapest, 1980. Akad. Kiado.´ [3028] A. Prekopa. Optimization under probabilistic constraints and its applications in statistics. In Com- putational statistics, Proc. 6th Symp., Prague 1984, 446-457, 1984. [3029] A. Prekopa.´ Numerical solution of probabilistic constrained programming problems. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 123–139. Springer, Berlin, 1988. [3030] A. Prekopa.´ Dual method for the solution of a one-stage stochastic programming problem with random RHS obeying a discrete probability distribution. Z. Oper. Res., 34(6):441–461, 1990. [3031] A. Prekopa´ and P. Kelle. Reliability type inventory models based on stochastic programming. In Survey of mathematical programming (Proc. Ninth Internat. Math. Programming Sympos., Bu- dapest, 1976), Vol. 2, pages 167–182. North-Holland, Amsterdam, 1979.

170 [3032] A. Prekopa and A. Ruszczynski, editors. Special Issue on Stochastic Programming. Taylor & Fran- cis Group, London, etc., 2002. Optimization Methods and Software (OMS), Volume 17, Number 3. [3033] A. Prekopa´ and T. Szantai.´ On multi-stage stochastic programming (with application to optimal control of water supply). In Progress in operations research, Vols. I, II (Proc. Sixth Hungarian Conf., Eger, 1974), pages 733–755. Colloq. Math. Soc. Janos´ Bolyai, Vol. 12, Amsterdam, 1976. North-Holland. [3034] A. Prekopa´ and T. Szantai.´ Flood control reservoir system design using stochastic programming. Math. Programming Stud., 9:138–151, 1978. Mathematical programming in use. [3035] A. Prekopa and T. Szantai. On optimal regulation of a storage level with application to the water level regulation of a lake. In Survey of mathematical programming, Proc. int. Symp., Vol. 2, Budapest 1976, 183-210, 1980. [3036] A. Prekopa´ and T. Szantai.´ Flood control reservoir system design using stochastic programming. Tanulmanyok—MTA´ Szamit´ astech.´ Automat. Kutato´ Int. Budapest, 167:155–177, 1985. Studies in applied stochastic programming, I. [3037] A. Prekopa´ and R.J.-B. Wets, editors. Stochastic programming 84. I, Amsterdam, 1986. North- Holland Publishing Co. Math. Programming Stud. No. 27 (1986). [3038] A. Prekopa´ and R.J.-B. Wets, editors. Stochastic programming 84. II, Amsterdam, 1986. North- Holland Publishing Co. Math. Programming Stud. No. 28 (1986). [3039] Andras´ Prekopa.´ Logarithmic concave measures with application to stochastic programming. Acta Sci. Math. (Szeged), 32:301–316, 1971. [3040] Andras´ Prekopa.´ A class of stochastic programming decision problems. Math. Operationsforsch. Statist., 3(5):349–354, 1972. [3041] Andras´ Prekopa.´ Laws of large numbers for random linear programs. Math. Systems Theory, 6:277–288, 1972. [3042] Andras´ Prekopa.´ Contributions to the theory of stochastic programming. Math. Programming, 4:202–221, 1973. [3043] Andras Prekopa. On logarithmic concave measures and functions. Acta Sci. math. 34, 335-343, 1973. [3044] Andras Prekopa. Programming under probabilistic constraints with a random technology matrix. Math. Operationsforsch. Statistik 5, 109-116, 1974. [3045] Andras Prekopa. New proof for the basic theorem of log concave measures. Alkalmazott Mat. Lapok 1, 385-389, 1977. [3046] Andras´ Prekopa,´ editor. Studies in applied stochastic programming. I. Magyar Tudomanyos´ Akademia,´ Budapest, 1978. Tanulmanyok—MTA´ Szamit´ astech.´ Automat. Kutato´ Int. Budapest No. 80 (1978). [3047] Andras´ Prekopa.´ Logarithmic concave measures and related topics. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 63–82. Academic Press, London, 1980. [3048] Andras´ Prekopa.´ Network planning using two-stage programming under uncertainty. In Recent results in stochastic programming (Proc. Meeting, Oberwolfach, 1979), volume 179 of Lecture Notes in Econom. and Math. Systems, pages 215–237. Springer, Berlin, 1980. [3049] Andras´ Prekopa.´ Stochastic programming models and their application. Tanulmanyok—MTA´ Szamit´ astech.´ Automat. Kutato´ Int. Budapest, 106:25, 1980.

171 [3050] Andras´ Prekopa.´ The use of stochastic programming for the solution of some problems in statistics and probability. In Extremal methods and systems analysis (Internat. Sympos., Univ. Texas, Austin, Tex., 1977), volume 174 of Lecture Notes in Econom. and Math. Systems, pages 522–538, Berlin, 1980. Springer. [3051] Andras´ Prekopa.´ Dynamic type stochastic programming models. Tanulmanyok—MTA´ Szamit´ astech.´ Automat. Kutato´ Int. Budapest, 167:179–209, 1985. Studies in applied stochastic programming, I. [3052] Andras´ Prekopa,´ editor. Studies in applied stochastic programming. I. MTA Szamit´ astechn.´ Au- tomat. Kutato´ Intezet,´ Budapest, 1985. Tanulmanyok—MTA´ Szamit´ astech.´ Automat. Kutato´ Int. Budapest No. 167 (1985). [3053] Andras´ Prekopa.´ Boole-Bonferroni inequalities and linear programming. Oper. Res., 36(1):145– 162, 1988. [3054] Andras´ Prekopa.´ Stochastic programming, volume 324 of Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht, 1995. [3055] Andras´ Prekopa.´ The use of discrete moment bounds in probabilistic constrained stochastic programming models. Ann. Oper. Res., 85:21–38, 1999. Stochastic programming. State of the art, 1998 (Vancouver, BC). [3056] Andras´ Prekopa.´ Discrete higher order convex functions and their applications. In Generalized convexity and generalized monotonicity (Karlovassi, 1999), pages 21–47. Springer, Berlin, 2001. [3057] Andras´ Prekopa.´ On the concavity of multivariate probability distribution functions. Oper. Res. Lett., 29(1):1–4, 2001. [3058] Andras Prekopa, Istvan Deak, Sandor Ganczer, and Karoly Patyi. The STABIL stochastic programming model and its experimental application to the electrical energy sector of the Hungarian economy. In Stochastic programming, Proc. int. Conf., Oxford 1974, 369-385, 1980. [3059] Andras´ Prekopa,´ Istvan´ Deak,´ Sandor´ Ganczer, and Karoly´ Patyi. The STABIL stochastic programming model and its experimental application to the electrical energy sector of the Hungarian economy. Tanulmanyok—MTA´ Szamit´ astech.´ Automat. Kutato´ Int. Budapest, 167:5–30, 1985. Studies in applied stochastic programming, I. [3060] Andras´ Prekopa,´ Sandor´ Ganczer, Istvan´ Deak,´ and Karoly´ Patyi. The stochastic programming model STABIL, and its experimental application to the Hungarian electrical power industry. Alka- lmaz. Mat. Lapok, 1(1-2):3–22, 1975. [3061] Andras´ Prekopa´ and Xiaoling Hou. A stochastic programming model to ﬁnd optimal sample sizes to estimate unknown parameters in an LP. Oper. Res. Lett., 32(1):59–67, 2004. [3062] Andras´ Prekopa´ and Peter´ Kelle. Inventory models of reliability type based on stochastic programming. Alkamaz. Mat. Lapok, 2(1-2):1–16, 1976. [3063] Andras´ Prekopa´ and Wenzhong Li. Solution of and bounding in a linearly constrained optimization problem with convex, polyhedral objective function. Math. Programming, 70(1, Ser. A):1–16, 1995. [3064] Andras´ Prekopa,´ Jianmin Long, and Tamas´ Szantai.´ New bounds and approximations for the probability distribution of the length of the critical path. In Dynamic stochastic optimization (Laxenburg, 2002), volume 532 of Lecture Notes in Econom. and Math. Systems, pages 293–320. Springer, Berlin, 2004. [3065] Andras´ Prekopa,´ Tamas´ Rapcsak,´ and Istvan´ Zsuffa. A new method for serially linked reservoir system design using stochastic programming. Tanulmanyok—MTA´ Szamit´ astech.´ Automat. Kutato´ Int. Budapest, 167:75–97, 1985. Studies in applied stochastic programming, I.

172 [3066] Andras´ Prekopa´ and Andrzej Ruszczynski,´ editors. Stochastic programming. Taylor & Francis Ltd., Reading, 2002. Optim. Methods Softw. 17 (2002), no. 3. [3067] Andras´ Prekopa´ and Tamas´ Szantai.´ A new multivariate gamma distribution and its fitting to empirical streamflow data. Tanulmanyok—MTA´ Szamit´ astech.´ Automat. Kutato´ Int. Budapest, 167:99– 118, 1985. Studies in applied stochastic programming, I. [3068] Andras´ Prekopa,´ Bela´ Vizvari,´ and Tamas´ Badics. Programming under probabilistic constraint with discrete random variable. In New trends in mathematical programming, pages 235–255. Kluwer Acad. Publ., Boston, MA, 1998. [3069] Daniele Pretolani. A directed hypergraph model for random time dependent shortest paths. Eu- ropean J. Oper. Res., 123(2):315–324, 2000. Advances in theory and practice of combinatorial optimization (Puerto de la Cruz, 1997). [3070] Geoffrey Pritchard and Golbon Zakeri. Upper bounds for Gaussian stochastic programs. Math. Program., 86(1, Ser. A):51–63, 1999. [3071] Fabio Privileggi. A characterization for solutions of stochastic discrete time optimization models. Riv. Mat. Sci. Econom. Social., 18(2):165–180, 1995. [3072] Fukakujissei o fukumu shisutemu ni okeru saitekika (Optimization methods for mathematical systems with uncertainty), Kyoto, 1997. Kyoto University Research Institute for Mathematical Sci- ences. Surikaisekikenky¯ usho¯ Koky¯ uroku¯ No. 978 (1997). [3073] L. Pronzato, H. P. Wynn, and A. A. Zhigljavsky. Finite sample behaviour of an ergodically fast line-search algorithm. Comput. Optim. Appl., 14(1):75–86, 1999. [3074] L. Pronzato, H.P. Wynn, and A.A. Zhigljavsky. Stochastic analysis of convergence via dynamic representation for a class of line-search algorithms. Combin. Probab. Comput., 6(2):205–229, 1997. [3075] Luc Pronzato. Adaptive optimization and D-optimum experimental design. Ann. Statist., 28(6):1743–1761, 2000. [3076] Luc Pronzato and Eric Walter. Experimental design for estimating the optimum point in a response surface. Acta Appl. Math., 33(1):45–68, 1993. Stochastic optimization. [3077] Luc Pronzato, Henry P. Wynn, and Anatoly A. Zhigljavsky. Dynamical search. Chapman & Hall/CRC, Boca Raton, FL, 2000. Applications of dynamical systems in search and optimization, Interdisciplinary statistics. [3078] Luc Pronzato, Henry P. Wynn, and Anatoly A. Zhigljavsky. Dynamical search. Chapman & Hall/CRC, Boca Raton, FL, 2000. Applications of dynamical systems in search and optimization, Interdisciplinary statistics. [3079] A.I. Propoi and A.V. Pukhlikov. The stochastic Newton method in nonlinear extremal problems. Avtomat. i Telemekh., 4:85–95, 1993. [3080] A. V. Protasov and V. A. Ogorodnikov. Dynamic probabilistic method of numerical modeling of stochastic multidimensional fields. In International Conference on Computational Mathematics. Part I, II, pages 259–263. ICM&MG Pub., Novosibirsk, 2002. [3081] I.M. Prudnikov. A method for the global optimization of a function and an estimate for the rate of its convergence. Avtomat. i Telemekh., 12:72–81, 1993. [3082] B.N. Pshenichnyj and V.G. Pokotilo. On a linear object observation problem. J. Appl. Math. Mech. 46, 156-160 translation from Prikl. Mat. Mekh. 46, 212-217 (1982)., 1983.

173 [3083] V.A. Pukas. Distribution of active loading in a power system as a two-stage nonlinear stochastic programming problem. Trudy Akad. Nauk Litov. SSR Ser. B, 5(84):147–156, 1974. [3084] Madan L. Puri and Dan A. Ralescu. Differentielle´ d’une fonction floue. C.R. Acad. Sci. Paris Ser.´ I Math., 293(4):237–239, 1981. [3085] M.C. Puri. Extreme point enumeration technique for assignment problem. Portugal. Math., 37(1- 2):31–37 (1981), 1978. [3086] Martin L. Puterman. Markov decision processes. In Stochastic models, Handb. Oper. Res. Manage. Sci. 2, 331-434, 1990. [3087] Yu. P. Pyt’ev. Nonlinear reduction of a measurement. Mat. Model., 1(5):44–59, 158, 1989. [3088] Li Qun Qi. An alternating method for stochastic linear programming with simple recourse. Math. Programming Stud., 27:183–190, 1986. Stochastic programming 84. I. [3089] Li Qun Qi. The A-forest iteration method for the stochastic generalized transportation problem. Math. Oper. Res., 12(1):1–21, 1987. [3090] Li Qun Qi and Xiao Ming Tu. The dual forest iteration method for stochastic transportation problems. J. Tsinghua Univ., 28(3):74–82, 1988. [3091] Li Qun Qi and Robert S. Womersley. An SQP algorithm for extended linear-quadratic problems in stochastic programming. Ann. Oper. Res., 56:251–285, 1995. Stochastic programming (Udine, 1992). [3092] Liqun Qi. Forest iteration method for stochastic transportation problem. Math. Program. Study 25, 142-163, 1985. [3093] Shi Xian Qian. Generalization of least-square isotonic regression. J. Statist. Plann. Inference, 38(3):389–397, 1994. [3094] Chang Ge Qiao. Convergence analysis of a stochastic parallel algorithm. J. Numer. Methods Comput. Appl., 17(4):308–312, 1996. [3095] J. Qiu and A. A. Girgis. Optimization of power-system reliability level by stochastic-programming. Electric Power Systems Research, 26(2):87–95, 1993. [3096] Hualin Qu and Shiying Zhang. Stochastic generalized goal programming. Trans. Tianjin Univ., 1(2):129–132, 1995. [3097] J.P. Quadrat. On optimal stochastic control problem of large systems. In Advances in filtering and optimal stochastic control, Proc. IFIP-WG 7/1 Work. Conf., Cocoyoc/Mex. 1982, Lect. Notes Contr. Inf. Sci. 42, 312-325 , 1982. [3098] J.P. Quadrat and M. Viot. Approximation numerique des problemes de programmation dynamique stochastique. IRIA, Cahier No.9, 201-224, 1972. [3099] J.P. Quadrat and M. Viot. Methodes de simulation en programmation dynamique stochastique. Revue Franc. Automat. Inform. Rech. operat. 7, R-1, 3-22, 1973. [3100] Guillaume Rabault. When do borrowing constraints bind? Some new results on the income fluctuation problem. J. Econom. Dynam. Control, 26(2):217–245, 2002. [3101] S.T. Rachev and W. Romisch,¨ editors. Stochastic Programming: Stability, Numerical Methods and Applications. 1994. J. of Computational and Applied Mathematics 56, No. 1–2. [3102] Svetlozar T. Rachev and Werner Romisch.¨ Quantitative stability in stochastic programming: the method of probability metrics. Math. Oper. Res., 27(4):792–818, 2002.

174 [3103] Rudiger¨ Rackwitz. Comparison of gradient-free optimizers in structural reliability analysis. In Stochastic optimization techniques (Neubiberg/Munich, 2000), volume 513 of Lecture Notes in Econom. and Math. Systems, pages 309–319. Springer, Berlin, 2002. [3104] S. Raczynski. Stochastic optimization algorithm for nonlinear discrete models of production systems. Probl. Control Inf. Theory 7, 443-458 (Russian), Suppl. 1-14 (English), 1978. [3105] F.J. Radermacher. Cost-dependent essential systems of ES-strategies for stochastic scheduling problems. Methods Oper. Res. 42, 17-31, 1981. [3106] A. Ye. Radiyevskiy. A stochastic multicriterial optimization problem. J. Automat. Inform. Sci., 25(4):28–30 (1993), 1992. [3107] Yu. S. Ragimov. On a decision-making problem in operations with random factors. In Numerical methods in optimization and analysis (Russian) (Irkutsk, 1989), pages 41–46. “Nauka” Sibirsk. Otdel., Novosibirsk, 1992. [3108] Yu.S. Ragimov. The principle of maximal guaranteed result in operations with random factors. Teor. Slozhnykh Sist. Metody Model. 1979, 64-76, 1979. [3109] E. Raik. Qualitative investigations in problems of stochastic nonlinear programming. Eesti NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 20:8–14, 1971. [3110] E. Raik. The quantile function in stochastic nonlinear programming. Eesti NSV Tead. Akad. Toime- tised Fuüs.-Mat.¨ , 20:229–231, 1971. [3111] E. Raik. Problems of stochastic programming with probability and quantile functionals. Eesti NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 21:142–148, 1972. [3112] E. Raik. Stochastic programming problems with decision functions. Eesti NSV Tead. Akad. Toime- tised Fuüs.-Mat.¨ , 21:258–263, 1972. [3113] E.` Raik. Differentiability of a probability function with respect to a parameter, and a stochastic pseudogradient method of optimizing it. Eesti NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 24(1):5–9, 1975. [3114] V. Raik, E.` The structure of optimal randomized solutions of stochastic programming problems. Kibernetika (Kiev), 2:95–98, 1976. [3115] W.M. Raike. Dissection methods for solutions in chance constrained programming problems under discrete distributions. Management Sci., Theory 16, 708-715, 1970. [3116] Sanguthevar Rajasekaran and John H. Reif. Nested annealing: a provable improvement to simulated annealing. Theoret. Comput. Sci., 99(1):157–176, 1992. [3117] Eh. Rajk. Comparison of solutions in different formulations of stochastic programming problems. Izv. Akad. Nauk Ehst. SSR, Fiz. Mat. 19, 469-472, 1970. [3118] Eh. Rajk. Ungleichungen in Aufgaben der stochastischen Programmierung. Izv. Akad. Nauk Ehst. SSR, Fiz. Mat. 19, 292-298, 1970. [3119] Eh. Rajk. On quantile function in stochastic nonlinear programming problems. Izv. Akad. Nauk Ehst. SSR, Fiz. Mat. 20, 229-231, 1971. [3120] Terry R. Rakes and Gary R. Reeves. Selecting tolerances in chance-constrained programming: a multiple objective linear programming approach. Oper. Res. Lett., 4(2):65–69, 1985. [3121] Katrien Ramaekers, Gerrit K. Janssens, and Hendrik Van Landeghem. Towards logistics systems parameter optimisation through the use of response surfaces. 4OR, 4(4):331–342, 2006.

175 [3122] Aparna Ramanathan and Charles J. Colbourn. Bounds for all-terminal reliability by arc-packing. Ars Combin., 23(A):229–236, 1987. [3123] Jorg¨ Rambau. Deferment Control for Reoptimization – How to Find Fair Reoptimized Dispatches. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algo- rithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [3124] Jaroslav Ramik and Josef Rimanek. Vaguely formulated coefficients of linear inequalities. BUSE- FAL 15, 20-24, 1983. [3125] Jaroslav Ramik and Josef Rimanek. Fuzzy parameters in optimal allocation of resources. In Op- timization models using fuzzy sets and possibility theory, Theory Decis. Libr., Ser. B 4, 359-374, 1987. [3126] Ya. Ramik and J. Rimanek. Linear constraints with inexact data. Sov. J. Comput. Syst. Sci. 25, No.5, 90-98 translation from Izv. Akad. Nauk SSSR, Tekh. Kibern. 1987, No.2, 41-48 (1987)., 1987. [3127] J.A. Ramos. A Kalman-tracking filter approach to nonlinear programming. Comput. Math. Appl. 19, No.11, 63-74, 1990. [3128] Oma Rani and R.N. Kaul. Nonlinear programming in complex space. J. math. Analysis Appl. 43, 1-14, 1973. [3129] G.V. Rao. On dynamic programming and risk functions. Cahiers Centre Etud. Rech. oper. 14, 88-104, 1972. [3130] P.K. Rao and K.S. Reddy. Optimal economic growth under uncertainty with time-lags. Internat. J. Systems Sci. 6, 793-797, 1975. [3131] Shivaji Rao and George O.IV Schneller. On the stochastic non-sequential production-planning problem. J. Oper. Res. Soc. 41, No.3, 241-247, 1990. [3132] S.S. Rao. Structural optimization by chance constrained programming techniques. Comput. Struct. 12, 777-781, 1980. [3133] Tamas´ Rapcsak.´ An exterior-point algorithm for solution of convex nonlinear programming problems. Alkalmaz. Mat. Lapok, 1(3–4):357–364, 1975. [3134] Tamas Rapcsak and Peter Borzsak. On the concavity set of the product functions. Alkalmazott Mat. Lapok 11, 311-318, 1985. [3135] E.` O. Rapoport. Asymptotic properties of a test connected with a random partition of an interval. Optimizatsiya, 35(52):28–35, 158, 1985. [3136] G. Rappl. Optimierung durch Zufallsrichtungsverfahren., 1980. [3137] L.A. Rastrigin. Mixed algorithms of random search. In Problems of random search, 2 (Russian), pages 8–17, 219. Izdat. “Zinatne”, Riga, 1973. [3138] L.A. Rastrigin. Particularities of the calculation of bounds in random search processes. Problemy Sluchain. Poiska, 7:13–21, 317, 1978. Adaptation problems in technical systems (Russian). [3139] L.A. Rastrigin. Adaptation of complex systems. Methods and applications. (Adaptatsiya slozhnykh sistem. Metody i prilozheniya). Akademiya Nauk Latvijskoj SSR. Institut Ehlektroniki i Vychisli- tel’noj Tekhniki. Riga: ”Zinatne”., 1981. [3140] L.A. Rastrigin. Sequential binary random search in problems of stochastic programming. Soviet J. Comput. Systems Sci., 25(5):163–172, 1987.

176 [3141] L.A. Rastrigin and A.V. Samchenko. Application of the mechanisms of natural evolution for the solution of optimization problems. Dinamika Sistem, 195:163–174, 1984. [3142] R. Ravi and Amitabh Sinha. Hedging uncertainty: approximation algorithms for stochastic optimization problems. In Integer programming and combinatorial optimization, volume 3064 of Lecture Notes in Comput. Sci., pages 101–115. Springer, Berlin, 2004. [3143] R. Ravi and Amitabh Sinha. Hedging uncertainty: approximation algorithms for stochastic optimization problems. Math. Program., 108(1, Ser. A):97–114, 2006. [3144] Daniel J. Reaume, H. Edwin Romeijn, and Robert L. Smith. Implementing pure adaptive search for global optimization using Markov chain sampling. J. Global Optim., 20(1):33–47, 2001. [3145] M. C. Recchioni and A. Scoccia. A stochastic algorithm for constrained global optimization. J. Global Optim., 16(3):257–270, 2000. [3146] Giovanna Redaelli. Convergence problems in stochastic programming models with probabilistic constraints. Riv. Mat. Sci. Econom. Social., 21(1-2):147–164, 1998. [3147] Giovanna Redaelli. Vector stochastic optimization problems. In Generalized convexity and generalized monotonicity (Karlovassi, 1999), volume 502 of Lecture Notes in Econom. and Math. Systems, pages 362–380. Springer, Berlin, 2001. [3148] R.-R. Redetzky. Stabilitaetsanalyse der stochastischen linearen Optimierung (SLO). I. Wiss. Z. techn. Hochschule Ilmenau 22, 31-64, 1976. [3149] R.-R. Redetzky. Stabilitaetsanalyse der stochastischen linearen Optimierung (SLO). II. Wiss. Z. Techn. Hochschule Ilmenau 23, No.6, 111-135, 1977. [3150] R.-R. Redetzky. Der gegenwartige¨ Stand beim Verteilungsproblem der stochastischen linearen Optimierung. I. Wiss. Z. Tech. Hochsch. Ilmenau, 25(1):75–104, 1979. [3151] R.-R. Redetzky. Zum gegenwartigen¨ Stand beim Verteilungsproblem der stochastischen linearen Optimierung. II. Wiss. Z. Tech. Hochsch. Ilmenau, 27(1):109–141, 1981. [3152] Robert Redetzky. Ueber Dualitaetsaussagen in der stochastischen linearen Optimierung (SLO). (On duality in stochastic linear optimization (SLO)). Wiss. Z. Tech. Hochschule Ilmenau 16, No.5, 7-16, 1970. [3153] R.R. Redetzky. Verteilungsproblem der stochastischen linearen Optimierung. In 21. int. wiss. Kolloq.; Ilmenau 1976, Heft 3, 81-84, 1976. [3154] Dieter Armin Reetz. Kontrahierende endliche Markoffsche Entscheidungsprozesse. Berlin: Guenter Marchal und Hans-Jochen Matzenbacher, Wissenschaftsverlag., 1980. [3155] J. Reinhart. Implementation of the response surface method (RSM) for stochastic structural optimization problems. In Stochastic programming methods and technical applications (Neu- biberg/Munich, 1996), pages 394–409. Springer, Berlin, 1998. [3156] Juergen Th. Rembold. Stochastische lineare Optimierung. Eine anwendungsbezogene systematische Darstellung. Mathematical Systems in Economics. 31. Meisenheim am Glan: Verlag Anton Hain., 1977. [3157] Juergen Th. Rembold. Stochastische Engpassprobleme. Technical report, Mathematisch- Naturwissenschaftliche Fakultaet der Universitaet zu Koeln. 154 S., 1978. [3158] Jurgen¨ Th. Rembold. Stochastische lineare Optimierung. Verlag Anton Hain, Meisenheim am Glan, 1977. Eine anwendungsbezogene systematische Darstellung, Mathematical Systems in Eco- nomics, No. 31.

177 [3159] C. Renotte, A. Vande Wouwer, and M. Remy. Neural modeling and control of a heat exchanger based on SPSA. In Proceedings of the American Control Conference, pages 3299–3303, 2000. [3160] L.K. Repina and V.N. Solncev. Solution of two applied problems by the method of random search. In Operations research and statistical modeling, No. 1 (Russian), pages 136–145. Izdat. Leningrad. Univ., Leningrad, 1972. [3161] M. Resh. Chance constrained programming of the machine loading problem with stochastic processing times. Management Sci., 17:48–65, 1970/71. [3162] Michael Resh and Moshe Friedman. Stochastic programming of multiple channel service systems with deterministic inflow and stochastic service times. Management Sci., 22(9):1022–1033, 1975/76. [3163] C. ReVelle and K. Hogan. A reliability-constrained siting model with local estimates of busy fractions. Environment and Planning B: Planning and Design, 15(3):143–152, 1988. [3164] F. Rezayat. On the use of an SPSA-based model-free controller in quality improvement. Automat- ica, 31:913–915, 1995. [3165] F. Rezayat. Constrained SPSA controller for operations processes. IEEE Transactions on Systems, Man, and Cybernetics?A, 29:645–649, 1999. [3166] K. Reznicek and T.C.E. Cheng. Stochastic modelling of reservoir operations. Eur. J. Oper. Res. 50, No.3, 235-248, 1991. [3167] WanSoo T. Rhee. Convergence of optimal stochastic bin packing. Oper. Res. Lett. 4, 121-123, 1985. [3168] Wansoo T. Rhee. A note on asymptotic properties of the quadratic assignment problem. Oper. Res. Lett. 7, No.4, 197-200, 1988. [3169] Wansoo T. Rhee. Optimal bin packing with items of random sizes. Math. Oper. Res. 13, No.1, 140-151, 1988. [3170] WanSoo T. Rhee. On the fluctuations of the stochastic traveling salesperson problem. Math. Oper. Res., 16(3):482–489, 1991. [3171] WanSoo T. Rhee. Stochastic analysis of a modified first fit decreasing packing. Math. Oper. Res., 16(1):162–175, 1991. [3172] WanSoo T. Rhee. Optimal bin packing of items of sizes uniformly distributed over [0,1]. Math. Oper. Res. 18, No.3, 694-704, 1993. [3173] Wansoo T. Rhee. Probabilistic analysis of a capacitated vehicle routing problem. I. Optimization 27, No.1-2, 79-87, 1993. [3174] WanSoo T. Rhee and Michel Talagrand. Martingale inequalities, interpolation and NP-complete problems. Math. Oper. Res., 14(1):91–96, 1989. [3175] WanSoo T. Rhee and Michel Talagrand. Dual bin packing with items of random sizes. Math. Programming, 58(2, Ser. A):229–242, 1993. [3176] Wansoo T. Rhee and Michel Talagrand. On-line bin packing of items of random sizes. II. SIAM J. Comput. 22, No.6, 1251-1256, 1993. [3177] WanSoo T. Rhee and Michel Talagrand. On-line bin packing with items of random size. Math. Oper. Res., 18(2):438–445, 1993. [3178] W.T. Rhee. Inequalities for bin packing. III. Optimization 29, No.4, 381-385, 1994.

178 [3179] W.T. Rhee and M. Talagrand. Multidimensional optimal bin packing with items of random size. Mathematics of Operations Research, 16(3):490–503, 1991. [3180] Ulrich Rieder and Rudi Zagst. Monotonicity and bounds for convex stochastic control models. Z. Oper. Res., 39(2):187–207, 1994. [3181] Rhonda Righter. Job scheduling to minimize expected weighted ﬂowtime on uniform processors. Syst. Control Lett. 10, No.4, 211-216, 1988. [3182] Rhonda Righter. Stochastically maximizing the number of successes in a sequential assignment problem. J. Appl. Probab., 27(2):351–364, 1990. [3183] Rhonda Righter and Susan H. Xu. Scheduling jobs on non-identical IFR processors to minimize general cost functions. Adv. Appl. Probab. 23, No.4, 909-924, 1991. [3184] Morten Riis and Kim Allan Andersen. Applying the minimax criterion in stochastic recourse programs. European J. Oper. Res., 165(3):569–584, 2005. [3185] Morten Riis and Jørn Lodahl. A bicriteria stochastic programming model for capacity expansion in telecommunications. Math. Methods Oper. Res., 56(1):83–100, 2002. Special issue on combinatorial and integer programming. [3186] Morten Riis and Rudiger¨ Schultz. Applying the minimum risk criterion in stochastic recourse programs. Stochastic Programming E-Print Series, http://www.speps.org, 2001. [3187] A.H.G. Rinnooy Kan. Stochastic integer programming: the distribution problem. In Stochastic programming (Gargnano, 1983), volume 76 of Lecture Notes in Control and Inform. Sci., pages 140–150, Berlin, 1986. Springer. [3188] A.H.G. Rinnooy Kan and L. Stougie. Stochastic integer programming. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 201–213. Springer, Berlin, 1988. [3189] A.H.G. Rinnooy Kan and G.T. Timmer. Stochastic methods for global optimization. Amer. J. Math. Management Sci., 4(1-2):7–40, 1984. Statistics and optimization : the interface. [3190] Alexander H.G. Rinnooy Kan and Leen Stougie. On the relation between complexity and uncertainty. Ann. Oper. Res. 18, No.1-4, 17-23, 1989. [3191] Yosef Rinott. Convexity and optimization in certain problems in statistics. In Recent results in stochastic programming, Proc., Oberwolfach 1979, Lect. Notes Econ. Math. Syst. 179, 99-103, 1980. [3192] K.K. Ripa. Some statistic properties of optimizing automata and random search. Avtomat. Vychisl. Tekh., Riga 1970, No.3, 28-32, 1970. [3193] K.K. Ripa. Random search for the extremum of a multidimensional object as a stochastic automaton. In Problems of statistical optimization (Russsian), pages 15–30. Izdat. “Zinatne”, Riga, 1971. [3194] K.K. Ripa. A generalized algorithm of coordinate-wise adaptation of random search for the extremum. Problemy Sluchain. Poiska, 7:135–148, 318, 1978. Adaptation problems in technical systems (Russian). [3195] K.K. Ripa. A two-level algorithm of the adaptation of a random search for the extremum. Problemy Sluchain. Poiska, 7:159–183, 319, 1978. Adaptation problems in technical systems (Russian). [3196] Klaus Ritter. Approximation and optimization on the Wiener space. J. Complexity, 6(4):337–364, 1990.

179 [3197] Klaus Ritter and Stefan Schaffler.¨ A stochastic method for constrained global optimization. SIAM J. Optim., 4(4):894–904, 1994. [3198] Gianfranco Rizzo and Cesare Pianese. A stochastic approach for the optimization of open-loop engine control systems. Ann. Oper. Res., 31(1-4):545–568, 1991. Stochastic programming, Part II (Ann Arbor, MI, 1989). [3199] Werner Romisch¨ Robert Nurnberg.¨ A two-stage planning model for power scheduling in a hydro-thermal system under uncertainty. Stochastic Programming E-Print Series, http://www. speps.org, 2000. [3200] S.M. Robinson. Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity. Mathematical Programming Study, 30:45–66, 1987. [3201] Stephen M. Robinson. Extended scenario analysis. Ann. Oper. Res., 31(1-4):385–397, 1991. Stochastic programming, Part II (Ann Arbor, MI, 1989). [3202] Stephen M. Robinson. Analysis of sample-path optimization. Math. Oper. Res., 21(3):513–528, 1996. [3203] Stephen M. Robinson and Roger J.-B. Wets. Stability in two-stage stochastic programming. SIAM J. Control Optim., 25(6):1409–1416, 1987. [3204] R. T. Rockafellar. Duality and optimality in multistage stochastic programming. Ann. Oper. Res., 85:1–19, 1999. Stochastic programming. State of the art, 1998 (Vancouver, BC). [3205] R. Tyrrell Rockafellar, Stan Uryasev, and Michael Zabarankin. Optimality conditions in portfolio analysis with general deviation measures. Math. Program., 108(2-3, Ser. B):515–540, 2006. [3206] R. Tyrrell Rockafellar and Roger J.B. Wets. Continuous versus measurable recourse in N-stage stochastic programming. J. Math. Anal. Appl., 48:836–859, 1974. [3207] R.T. Rockafellar. Lagrange multipliers for an N-stage model in stochastic convex programming. In Analyse convexe Appl., Lecture Notes Econ. math. Syst. 102, 180-187 , 1974. [3208] R.T. Rockafellar. On the equivalence of multistage recourse models in stochastic optimization. In Control theory, numerical methods and computer systems modelling (Internat. Sympos., IRIA LABORIA, Rocquencourt, 1974), pages 314–321. Lecture Notes in Econom. and Math. Systems, Vol. 107, Berlin, 1975. Springer. [3209] R.T. Rockafellar. Computational schemes for large-scale problems in extended linear- quadratic programming. Math. Program., Ser. B 48, No.3, 447-474, 1990. [3210] R.T. Rockafellar and R.J.-B. Wets. Stochastic convex programming: Kuhn-Tucker conditions. J. Math. Econom., 2(3):349–370, 1975. [3211] R.T. Rockafellar and R.J.-B. Wets. Nonanticipativity and l1-martingales in stochastic optimization problems. Math. Programming Stud., 6:170–187, 1976. Stochastic systems: modeling, identification and optimization, II (Proc. Sympos., Univ Kentucky, Lexington, Ky., 1975). [3212] R.T. Rockafellar and R.J.-B. Wets. Stochastic convex programming: basic duality. Pacific J. Math., 62(1):173–195, 1976. [3213] R.T. Rockafellar and R.J.-B. Wets. Stochastic convex programming: relatively complete recourse and induced feasibility. SIAM J. Control Optimization, 14(3):574–589, 1976. [3214] R.T. Rockafellar and R.J.-B. Wets. Stochastic convex programming: singular multipliers and extended duality singular multipliers and duality. Pacific J. Math., 62(2):507–522, 1976.

180 [3215] R.T. Rockafellar and R.J.-B. Wets. Measures as Lagrange multipliers in multistage stochastic programming. J. Math. Anal. Appl., 60(2):301–313, 1977. [3216] R.T. Rockafellar and R.J.-B. Wets. The optimal recourse problem in discrete time: L1-multipliers for inequality constraints. SIAM J. Control Optimization, 16(1):16–36, 1978. [3217] R.T. Rockafellar and R.J.-B. Wets. Deterministic and stochastic optimization problems of Bolza type in discrete time. Stochastics, 10(3-4):273–312, 1983. [3218] R.T. Rockafellar and R.J.-B. Wets. A Lagrangian ﬁnite generation technique for solving linear- quadratic problems in stochastic programming. Math. Programming Stud., 28:63–93, 1986. Stochastic programming 84. II. [3219] R.T. Rockafellar and R.J.-B. Wets. Linear-quadratic programming problems with stochastic penalties: The ﬁnite generation algorithm. In Stochastic optimization, Proc. Int. Conf., Kiev/USSR 1984, Lect. Notes Control Inf. Sci. 81, 545-560, 1986. [3220] R.T. Rockafellar and R.J.-B. Wets. A note about projections in the implementation of stochastic quasigradient methods. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 385–392. Springer, Berlin, 1988. [3221] R.T. Rockafellar and R.J.-B. Wets. Generalized linear-quadratic problems of deterministic and stochastic optimal control in discrete time. SIAM J. Control Optim., 28(4):810–822, 1990. [3222] R.T. Rockafellar and Roger J.-B. Wets. A dual solution procedure for quadratic stochastic programs with simple recourse. In Numerical methods (Caracas, 1982), volume 1005 of Lecture Notes in Math., pages 252–265. Springer, Berlin, 1983. [3223] R.T. Rockafellar and Roger J.-B. Wets. Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res., 16(1):119–147, 1991. [3224] R.T. Rockafellar and Roger J.-B. Wets. A dual strategy for the implementation of the aggregation principle in decision making under uncertainty. Appl. Stochastic Models Data Anal., 8(3):245–255, 1992. [3225] N. Ye Rodnishchev. Method of feasible directions in optimization problems for stochastic systems. Engrg. Cybernetics, 10(1):29–34, 1972. [3226] J.R. Rodriguez-Mancilla and William T. Ziemba. The duality of option investment strategies for hedge funds. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [3227] W. Roedder. Ein Loesungsvorschlag fuer ein stochastisches Zielprogramm. In Operations Res.- Verf. 13, IV. Oberwolfach-Tag. Operations Res. 1971, 321- 328, 1972. [3228] W. Roedder. Loesungsvorschlaege fuer stochastische Zielprogramme. In Proc. Oper. Res., DGU Ann. Meet. 1971, 166-176, 1972. [3229] W. Roemisch and R. Schultz. Quantitative stability of two-stage stochastic programs. Z. Angew. Math. Mech. 74, No.6, T587-T589, 1994. [3230] Werner Roemisch. An approximation method in stochastic optimization and control. In Mathe- matical control theory, Banach Cent. Publ. 14, 477-490, 1985. [3231] N.V. Roenko. A stochastic problem of optimal placement of objects. Issled. Operatsii i ASU, 23:19–26, 139, 1984. [3232] H. Edwin Romeijn. Global optimization by random walk sampling methods, volume 32 of Tinber- gen Institute Research Series. Thesis Publishers, Amsterdam, 1992.

181 [3233] H. Edwin Romeijn and Dolores Romero Morales. A probabilistic analysis of the multi-period single-sourcing problem. Discrete Appl. Math., 112(1-3):301–328, 2001. Combinatorial Opti- mization Symposium (Brussels, 1998). [3234] H. Edwin Romeijn and Nanda Piersma. A probabilistic feasibility and value analysis of the generalized assignment problem. J. Comb. Optim., 4(3):325–355, 2000. [3235] W. Romisch.¨ On the convergence of measurable selections and an application to approximations in stochastic optimization. Z. Anal. Anwendungen, 5(3):277–288, 1986. [3236] W. Romisch¨ and R. Schultz. Distribution sensitivity for certain classes of chance-constrained models with application to power dispatch. J. Optim. Theory Appl., 71(3):569–588, 1991. [3237] W. Romisch¨ and R. Schultz. Multistage stochastic integer programs: An introduction. In M. Grotchel,¨ S.O. Krumke, and J. Rambau, editors, Online Optimization of Large Scale Systems, pages 581–600. Springer, Berlin, 2001. [3238] Werner Romisch.¨ On discrete approximations in stochastic programming. In Proceedings of the 13th Annual Conference on Mathematical Optimization (Berlin, 1981), volume 39 of Seminar- berichte, pages 166–175. Humboldt Univ. Berlin, 1982. [3239] Werner Romisch.¨ On convergence rates of approximations in stochastic programming. In 17. Jahrestagung “Mathematische Optimierung” (Sellin, 1984), volume 80 of Seminarberichte, pages 82–91. Humboldt Univ. Berlin, 1986. [3240] Werner Romisch.¨ Stability analysis of stochastic programs. Investigacion´ Oper., 14(2-3):175–194, 1993. Workshop on Stochastic Optimization: the State of the Art (Havana, 1992). [3241] Werner Romisch¨ and Rudiger¨ Schultz. On distribution sensitivity in chance constrained programming. In Advances in mathematical optimization, volume 45 of Math. Res., pages 161–168, Berlin, 1988. Akademie-Verlag. [3242] Werner Romisch¨ and Rudiger¨ Schultz. Stochastic programs with complete recourse: stability and an application to power dispatch. In System modelling and optimization (Leipzig, 1989), volume 143 of Lecture Notes in Control and Inform. Sci., pages 688–696. Springer, Berlin, 1990. [3243] Werner Romisch¨ and Rudiger¨ Schultz. Distribution sensitivity in stochastic programming. Math. Programming, 50(2, (Ser. A)):197–226, 1991. [3244] Werner Romisch¨ and Rudiger¨ Schultz. Stability analysis for stochastic programs. Ann. Oper. Res., 30(1-4):241–266, 1991. Stochastic programming, Part I (Ann Arbor, MI, 1989). [3245] Werner Romisch¨ and Rudiger¨ Schultz. Stability of solutions for stochastic programs with complete recourse. Math. Oper. Res., 18(3):590–609, 1993. [3246] Werner Romisch¨ and Rudiger¨ Schultz. Lipschitz stability for stochastic programs with complete recourse. SIAM J. Optim., 6(2):531–547, 1996. [3247] Werner Romisch¨ and Rudiger¨ Schultz. *Multistage stochastic integer programs: an introduction. In Online optimization of large scale systems, pages 581–622. Springer, Berlin, 2001. [3248] Werner Romisch¨ and Anton Wakolbinger. Obtaining convergence rates for approximations in stochastic programming. In Parametric optimization and related topics (Plaue, 1985), volume 35 of Math. Res., pages 327–343. Akademie-Verlag, Berlin, 1987. [3249] Werner Romisch¨ and Roger J.-B. Wets. Stability of -approximate solutions to convex stochastic programs. Stochastic Programming E-Print Series, http://www.speps.org, 2006. [3250] Heinrich Rommelfanger. Entscheiden bei Unschaerfe. Fuzzy Decision Support-Systeme. Springer- Verlag, 1988.

182 [3251] Heinrich Rommelfanger. Stochastic programming with vague data. Ann. Univ. Sci. Budapest. Sect. Comput., 12:213–221, 1991. Third IFSA-EC and EURO-WGFS Workshop on Fuzzy Sets (Visegrad,´ 1990). [3252] Heinrich Rommelfanger. Fuzzy mathematical programming. Modelling of vague data by fuzzy sets and solution procedures. In Bandemer, Hans (ed.), Modelling uncertain data. Berlin: Akademie Verlag, (ISBN 3-05-501578-9/pbk). Math. Res. 68, 142-152, 1992. [3253] Heinrich Rommelfanger. Entscheiden bei Unschaerfe. Fuzzy Decision Support-Systeme. (Decision- making in case of uncertainty. Decision-making in case of uncertainty).2., verb. u. erw. Aufl. Springer-Verlag, 1994. [3254] Mohammad Roosta. Routing through a network with maximum reliability. J. Math. Anal. Appl. 88, 341-347, 1982. [3255] Charles H. Rosa and Andrzej Ruszczynski.´ On augmented Lagrangian decomposition methods for multistage stochastic programs. Ann. Oper. Res., 64:289–309, 1996. Stochastic programming, algorithms and models (Lillehammer, 1994). [3256] Charles H. Rosa and Samer Takriti. Improving aggregation bounds for two-stage stochastic programs. Oper. Res. Lett., 24(3):127–137, 1999. [3257] Wanda Rosa-Hatko and Eldon Gunn. Some models of queueing control with switchover. Comput. Math. Appl. 21, No.11/12, 91-110, 1991. [3258] Scott L. Rosen and Catherine M. Harmonosky. An improved simulated annealing simulation optimization method for discrete parameter stochastic systems. Comput. Oper. Res., 32(2):343–358, 2005. [3259] Sheldon Ross. Introduction to stochastic dynamic programming. Probability and Mathematical Statistics. New York - London etc.: Academic Press., 1983. [3260] Francesco A. Rossi and Ilario Gavioli. Aspects of heuristic methods in the “Probabilistic Trav- eling Salesman Problem” (PTSP). In Stochastic in combinatorial optimization, Adv. Sch. CISM, Udine/Italy 1986, 214-227, 1987. [3261] V.I. Rotar’. Symmetric dependence, and a certain model for sample inspection. Ekonom.` i Mat. Metody, 9:1150–1156, 1973. [3262] V.I. Rotar’. On sufficient controls in dynamical problems of stochastic optimization. Mat. Zametki 40, No.4, 542-551, 1986. [3263] Marc Roubens and Jr. Teghem, Jacques. Comparison of methodologies for multicriteria feasibility—constrained fuzzy and multiple-objective stochastic linear programming. In Combin- ing fuzzy imprecision with probabilistic uncertainty in decision making, volume 310 of Lecture Notes in Econom. and Math. Systems, pages 240–265. Springer, Berlin, 1988. [3264] Marc Roubens and Jr. Teghem, Jacques. Comparison of methodologies for fuzzy and stochastic multi-objective programming. Fuzzy Sets and Systems, 42(1):119–132, 1991. [3265] B. Roy. Problems and methods with multiple objective functions. Math. Programming 1, 239-266, 1971. [3266] Santanu Roy. A note: “On income fluctuations and capital gains with a convex production function” [J. Econom. Dynam. Control 11 (1987), no. 3, 285–312; MR 88j:90067] by M. O. Sotomayor. J. Econom. Dynam. Control, 18(6):1199–1202, 1994. [3267] J. O. Royset and E. Polak. Implementable algorithm for stochastic optimization using sample average approximations. J. Optim. Theory Appl., 122(1):157–184, 2004.

183 [3268] Yu. A. Rozanov. On optimization of random functionals. In Control theory, numerical methods and computer systems modelling (Internat. Sympos., IRIA LABORIA, Rocquencourt, 1974), pages 192–206. Lecture Notes in Econom. and Math. Systems, Vol. 107, Berlin, 1975. Springer. [3269] Yuri A. Rozanov. A few methodological remarks on optimization random cost functions. Research memorandum. rm-73-7., Laxenburg, Austria: IIASA - International Institute for Applied Systems Analysis., 1973. [3270] G.B. Rubal’skij. Convolution operators conserving the property of the unimodality type for functions of one discrete variable. Cybernetics 24, No.3, 281-285 translation from Kibernetika 1988, No.3, 9-11 (1988)., 1988. [3271] E.Ya. Rubinovich. Trajectory control of observations in discrete stochastic optimization problems. Autom. Remote Control 41, 365-372 translation from Avtom. Telemekh. 1980, No.3, 93-102 (1980)., 1980. [3272] Ja. S. Rubinstein.ˇ The piecewise-linear representation of a function that is optimized in a noise environment. Avtomat. i Vycisl.ˇ Tehn., 5:36–43, 1968. [3273] Ja. S. Rubinsteinˇ and E.` K. Spilevskii.ˇ Asymptotic properties of a random search that is to be used for a search for the extremum of a function under conditions of noise. Voprosy Kibernet. Vycisl.ˇ Mat., 28:178–187, 1969. Problems of statistical optimization (Proc. Fifth All-Union Sem., Tashkent, 1968). [3274] Reuven Y. Rubinstein. Monte Carlo optimization, simulation and sensitivity of queueing networks. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. New York etc.: John Wiley & Sons, Inc., 1986. [3275] Reuven Y. Rubinstein. Combinatorial optimization, cross-entropy, ants and rare events. In Stochas- tic optimization: algorithms and applications (Gainesville, FL, 2000), pages 303–363. Kluwer Acad. Publ., Dordrecht, 2001. [3276] Reuven Y. Rubinstein and Alexander Shapiro. Discrete event systems. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons Ltd., Chichester, 1993. Sensitivity analysis and stochastic optimization by the score function method. [3277] R.Y. Rubinstein. Solution of nonlinear programming with unknown distribution function. Math. Comput. Simulation, 24(5):373–384, 1982. [3278] R.Y. Rubinstein. Smoothed functionals in stochastic optimization. Math. Oper. Res. 8, 26-33, 1983. [3279] R.Y. Rubinstein, S. Shapiro, and S. Uryasev. The score functions. In S.I. Gass and C.M. Harris, editors, Encyclopedia of Operations Research and Management Science, pages 614–617. Kluwer Academic Publishers, Boston/Dordrecht/London, 1996. [3280] Y. Rubinstein and A. Karnovsky. Local and integral properties of a search algorithm of the stochastic approximation type. Stochastic Processes Appl. 6, 124-134, 1978. [3281] Y. Rubinstein and A. Karnovsky. The regenerative method for constrained optimization problems. In Operational research ’78 (Proc. Eighth IFORS Internat. Conf., Toronto, Ont., 1978), pages 931–949. North-Holland, Amsterdam, 1979. [3282] Y.R. Rubinstein and G. Samorodnitsky. Efﬁciency of the random search method. Math. Comput. Simulation, 24(4):257–268, 1982. [3283] Ludger Ruschendorf¨ and Ludger Uckelmann. Numerical and analytical results for the transportation problem of Monge-Kantorovich. Metrika, 51(3):245–258 (electronic), 2000. [3284] Berc Rustem. Methods for optimal economic policy design. In Control and dynamic systems, Vol. 36, pages 17–74. Academic Press, San Diego, CA, 1990.

184 [3285] Ioan Rusu. On the solutions of a certain stochastic programming problem. In Proceedings of the Fourth Conference on Probability Theory (Bras¸ov, 1971), pages 583–586. Editura Acad. R.S.R., Bucharest, 1973. [3286] Ioan Rusu and Filia Cot¸iu. Sur un probleme` de programmation lineaire´ stochastique. In Trans- actions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions and the Eighth European Meeting of Statisticians (Tech. Univ, pages 457–463. Academia, Prague, 1978. [3287] A. Ruszczynski.´ A regularized decomposition method for minimizing a sum of polyhedral functions. Mathematical Programming, 35:309–333, 1986. [3288] A. Ruszczynski and A. Shapiro, editors. Stochastic Programming, volume 10 of Handbooks in Operations Research and Management Science. Elsevier, 2003. [3289] Andrzej Ruszczynski.´ Feasible direction methods for stochastic programming problems. Math. Programming, 19(2):220–229, 1980. [3290] Andrzej Ruszczynski.´ Stochastic feasible direction methods for nonsmooth stochastic optimization problems. Control Cybernet., 9(4):173–187 (1981), 1980. [3291] Andrzej Ruszczynski.´ A recursive quadratic programming algorithm for constrained stochastic programming problems. Control Cybernet., 13(1-2):59–72, 1984. [3292] Andrzej Ruszczynski.´ A method of feasible directions for solving nonsmooth stochastic programming problems. In Stochastic programming (Gargnano, 1983), volume 76 of Lecture Notes in Control and Inform. Sci., pages 258–271. Springer, Berlin, 1986. [3293] Andrzej Ruszczynski.´ A linearization method for nonsmooth stochastic programming problems. Math. Oper. Res., 12(1):32–49, 1987. [3294] Andrzej Ruszczynski.´ Modern techniques for linear dynamic and stochastic programs. In Aspira- tion based decision support systems, volume 331 of Lecture Notes in Econom. and Math. Systems, pages 48–67. Springer, Berlin, 1989. [3295] Andrzej Ruszczynski.´ Parallel decomposition of multistage stochastic programming problems. Math. Programming, 58(2, Ser. A):201–228, 1993. [3296] Andrzej Ruszczynski.´ On convergence of an augmented Lagrangian decomposition method for sparse convex optimization. Math. Oper. Res., 20(3):634–656, 1995. [3297] Andrzej Ruszczynski.´ On regularized duality in convex optimization. In Recent advances in nonsmooth optimization, pages 381–391, River Edge, NJ, 1995. World Sci. Publishing. [3298] Andrzej Ruszczynski.´ On the regularized decomposition method for stochastic programming problems. In Stochastic programming (Neubiberg/Munchen,¨ 1993), volume 423 of Lecture Notes in Econom. and Math. Systems, pages 93–108. Springer, Berlin, 1995. [3299] Andrzej Ruszczynski.´ Decomposition methods in stochastic programming. Math. Programming (Ser. B), 79(1-3):333–353, 1997. Lectures on mathematical programming (ismp97) (Lausanne, 1997). [3300] Andrzej Ruszczynski.´ Some advances in decomposition methods for stochastic linear programming. Ann. Oper. Res., 85:153–172, 1999. Stochastic programming. State of the art, 1998 (Van- couver, BC). [3301] Andrzej Ruszczynski.´ Probabilistic programs with discrete distributions and precedence constrained knapsack polyhedra. Stochastic Programming E-Print Series, http://www.speps. org, 2000.

185 [3302] Andrzej Ruszczynski.´ Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra. Math. Program., 93(2, Ser. A):195–215, 2002. [3303] Andrzej Ruszczynski´ and Alexander Shapiro. Conditional risk mappings. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [3304] Andrzej Ruszczynski´ and Alexander Shapiro. Optimization of convex risk functions. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [3305] Andrzej Ruszczynski´ and Alexander Shapiro. Optimization of convex risk functions. Math. Oper. Res., 31(3):433–452, 2006. [3306] Andrzej Ruszczynski´ and Alexander Shapiro. Corrigendum to: “Optimization of convex risk functions” [Math. Oper. Res. 31 (2006), no. 3, 433–452; mr2254417]. Math. Oper. Res., 32(2):496, 2007. [3307] Andrzej Ruszczynski´ and Wojciech Syski. A method of aggregate stochastic subgradients with on-line stepsize rules for convex stochastic programming problems. Math. Programming Stud., 28:113–131, 1986. Stochastic programming 84. II. [3308] Andrzej Ruszczynski and Robert J. Vanderbei. Frontiers of stochastically nondominated portfolios. Stochastic Programming E-Print Series, http://www.speps.org, 2002. [3309] David P. Rutenberg. Risk aversion in stochastic programming with recourse. Operations Res. 21, 377-380, 1973. [3310] V.I. Rymaruk. Stability of a stochastic programming method. Issled. Operatsii i ASU, 24:11–13, 110, 1984. [3311] V.I. Rymaruk. Stability of a class of quasigradient methods of solving minimax problems. In Methods in operations research and reliability theory, pages 3–6, 63, Kiev, 1985. Akad. Nauk Ukrain. SSR Inst. Kibernet. [3312] Oma M. Saad and Osama E. Imam. On the solution of stochastic multiobjective integer linear programming problems with a parametric study. Optimization Online, http://www. optimization-online.org, 2007. [3313] R.S. Sachan. Stochastic programming problems under risk and uncertainty. Cah. Cent. Etud. Rech. Oper. 12, 211-232, 1970. [3314] P. Sadegh and J.C. Spall. Optimal random perturbations for multivariate stochastic approximation using a simultaneous perturbation gradient approximation. In Proceedings of the American Control Conference, pages 3582–3586, 1997. [3315] P. Sadegh and J.C. Spall. Optimal sensor conﬁguration for complex systems. In Proceedings of the American Control Conference, pages 3575–3579, 1998. [3316] Payman Sadegh. Constrained optimization via stochastic approximation with a simultaneous perturbation gradient approximation. Automatica J. IFAC, 33(5):889–892, 1997. [3317] K.V. Sagatelyan. A probabilistic model of decision making. Erevan. Gos. Univ. Uchen. Zap. Estestv. Nauki, 3(166):16–21 (1988), 1987. [3318] Kemal H. Sahin and Urmila M. Diwekar. Better optimization of nonlinear uncertain systems (BONUS): a new algorithm for stochastic programming using reweighting through kernel density estimation. Ann. Oper. Res., 132:47–68, 2004. [3319] N. P. Sahoo and M. P. Biswal. Computation of probabilistic linear programming problems involving normal and log-normal random variables with a joint constraint. Int. J. Comput. Math., 82(11):1323–1338, 2005.

186 [3320] N. P. Sahoo and M. P. Biswal. Computation of some stochastic linear programming problems with Cauchy and extreme value distributions. Int. J. Comput. Math., 82(6):685–698, 2005. [3321] Gorkem Saka, Andrew J. Schaefer, and Lewis Ntaimo. Inverse stochastic linear programming. Optimization Online, http://www.optimization-online.org, 2007. [3322] Minoru Sakaguchi. A sequential assignment problem for randomly arrivin g jobs. Rep. statist. Appl. Res., Un. Japan Sci. Engin. 19, 99-109, 1972. [3323] Minoru Sakaguchi and Vesa Saario. A class of best-choice problems with full information. Math. Japon., 41(2):389–398, 1995. [3324] L. Sakalauskas. Towards implementable nonlinear stochastic programming. In Coping with uncertainty, volume 581 of Lecture Notes in Econom. and Math. Systems, pages 257–279. Springer, Berlin, 2006. [3325] L. Sakalauskas and K. Zilinskas.ˇ Application of the Monte-Carlo method to stochastic linear programming. In Computer aided methods in optimal design and operations, volume 7 of Ser. Comput. Oper. Res., pages 39–48. World Sci. Publ., River Edge, NJ, 2006. [3326] Leonidas Sakalauskas. Nonlinear stochastic optimization by the Monte-Carlo method. Informatica (Vilnius), 11(4):455–468, 2000. [3327] Leonidas Sakalauskas. Application of the Monte-Carlo method to nonlinear stochastic optimization with linear constraints. Informatica (Vilnius), 15(2):271–282, 2004. [3328] Leonidas L. Sakalauskas. Nonlinear stochastic programming by Monte-Carlo estimators. European J. Oper. Res., 137(3):558–573, 2002. [3329] L.L. Sakalauskas. On the convergence of a centering procedure. Litovsk. Mat. Sb., 31(4):670–677, 1991. [3330] Masatoshi Sakawa and Fumiko Seo. Interactive multiobjective decision-making in environmental systems using the fuzzy sequential proxy optimization technique. Large Scale Syst. 4, 223-243, 1983. [3331] Yu. P. Sakharov and A.P. Akulov. A method for nonlinear global optimization under conditions of uncertainty. Soobshch. Akad. Nauk Gruzin. SSR, 134(2):285–288, 1989. [3332] Abdellah Salhi, L. G. Proll, D. Rios Insua, and J. I. Martin. Experiences with stochastic algorithms for a class of constrained global optimisation problems. RAIRO Oper. Res., 34(2):183–197, 2000. [3333] G. Salinetti. Approximations for chance-constrained programming problems. Stochastics, 10(3- 4):157–179, 1983. [3334] G. Salinetti. Convergence of stochastic inﬁma: equi-semicontinuity. In Stochastic optimization (Kiev, 1984), volume 81 of Lecture Notes in Control and Inform. Sci., pages 561–575. Springer, Berlin, 1986. [3335] G. Salinetti. Semicontinuous random functions and random measures. Rend. Sem. Mat. Fis. Mi- lano, 57:465–482 (1989), 1987. [3336] G. Salinetti. Stochastic optimization and stochastic processes: the epigraphical approach. In Para- metric optimization and related topics (Plaue, 1985), volume 35 of Math. Res., pages 344–354. Akademie-Verlag, Berlin, 1987. [3337] G. Salinetti, W. Vervaat, and R.J.-B. Wets. On the convergence in probability of random sets (measurable multifunctions). Math. Oper. Res., 11(3):420–422, 1986.

187 [3338] Gabriella Salinetti. Consistency of statistical estimators: the epigraphical view. In Stochastic optimization: algorithms and applications (Gainesville, FL, 2000), pages 365–383. Kluwer Acad. Publ., Dordrecht, 2001. [3339] Gabriella Salinetti and Roger J.-B. Wets. On the convergence in distribution of measurable multifunctions (random sets), normal integrands, stochastic processes and stochastic infima. Math. Oper. Res., 11(3):385–419, 1986. [3340] David H. Salinger and R. Tyrrell Rockafellar. Dynamic splitting. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [3341] Paul A. Samuelson. Mathematics of speculative price. SIAM Review 15, 1-42, 1973. [3342] M. Sanchez, M.A. Gonzalez, and J. Sicilia. A model of a multivariable inventory. Rev. Acad. Canar. Cienc. 1, 201-215, 1990. [3343] M. Sanchez´ García and C. Gonzalez´ Martín. A global optimization algorithm based on the geometric probabilistic model. Application to a classification problem. Rev. Acad. Canaria Cienc., 3(1):33–44, 1991. [3344] Peter Sanders, Naveen Sivadasan, and Martin Skutella. Online Scheduling with Bounded Mi- gration. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl. de/05031, 2005. [3345] A. P. Sanghvi and I. H. Shavel. Investment planning for hydro-thermal power systems expansion: Stochastic programming employing the Dantzig-Wolfe decomposition principle. IEEE Transac- tions on Power Systems, 1(2):115–121, 1986. [3346] G. Santharam, P.S. Sastry, and M.A.L. Thathachar. Continuous action set learning automata for stochastic optimization. J. Franklin Inst. B, 331(5):607–628 (1995), 1994. [3347] Tjendera Santoso, Shabbir Ahmed, Marc Goetschalckx, and Alexander Shapiro. A stochastic programming approach for supply chain network design under uncertainty. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [3348] Tjendera Santoso, Shabbir Ahmed, Marc Goetschalckx, and Alexander Shapiro. A stochastic programming approach for supply chain network design under uncertainty. European J. Oper. Res., 167(1):96–115, 2005. [3349] M.S. Sarma. On the convergence of the Baba and Dorea random optimization methods. J. Optim. Theory Appl., 66(2):337–343, 1990. [3350] Hueseyin Sarper. Evaluation of the accuracy of Naslund’s approximation for managerial decision making under uncertainty. Appl. Math. Comput. 55, No.1, 73-87, 1993. [3351] Huseyin¨ Sarper. Monte Carlo simulation for analysis of the optimum value distribution in stochastic mathematical programs. Math. Comput. Simulation, 35(6):469–480, 1993. [3352] Tadeusz Sawik. Stochastic programming models of production-inventory problems. Arch. Autom. Telemech. 23, 115-127, 1978. [3353] Anureet Saxena. A short note on the probabilistic set covering problem. Stochastic Programming E-Print Series, http://www.speps.org, 2007. [3354] Anureet Saxena, Vineet Goyal, and Miguel Lejeune. Mip reformulations of the probabilistic set covering problem. Stochastic Programming E-Print Series, http://www.speps.org, 2007.

188 [3355] N.I. Scedrin and A.N. Karhov. Mathematische Methoden der Programmierung in der Oekonomik. (Matematiceskie metody programmirovanija v ekonomike.). Matematiceskaja statistika dlja ekonomistov. Moskau: ’Statistika’., 1974. [3356] Manfred Schael. Utility functions and optimal policies in sequential decision problems. In Game theory and mathematical economics, Proc. Semin., Bonn/Hagen 1980, 357-365, 1981. [3357] Manfred Schael. On dynamic programming under uncertainty. In Operations research, Proc. 10th Annu. Meet., Goettingen 1981, 415-422 , 1982. [3358] Manfred Schael. Markovian decision models with bounded finite-stage rewards. In Operations research, Proc. 12th Annu. Meet., Mannheim 1983, 470-474 , 1984. [3359] Manfred Schael. On stochastic dynamic programming: A bridge between Markov decision processes and gambling. In Markov processes and control theory, Proc. Symp., ISAM, Gaussig/GDR 1988, Math. Res. 54, 178-216, 1989. [3360] Guido Schafer¨ and Naveen Sivadasan. Topology Matters: Smoothed Competitiveness of Metrical Task Systems. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl. de/05031, 2005. [3361] S. Schaffler.¨ Unconstrained global optimization using stochastic integral equations. Optimization, 35(1):43–60, 1995. [3362] S. Schaffler,¨ R. Schultz, and K. Weinzierl. Stochastic method for the solution of unconstrained vector optimization problems. J. Optim. Theory Appl., 114(1):209–222, 2002. [3363] Stefan Schaffler.¨ Large-scale global optimization on transputer networks. In Applied mathematics and parallel computing, pages 275–290. Physica, Heidelberg, 1996. [3364] I.P. Schagen. The use of stochastic processes in interpolation and approximation. Internat. J. Comput. Math., 8(1):63–76, 1980. [3365] I.P. Schagen. Sequential exploration of unknown multidimensional functions as an aid to optimization. IMA J. Numer. Anal., 4(3):337–347, 1984. [3366] Manfred Schal.¨ Existence of optimal policies in stochastic dynamic programming. In Proceedings of the Sixth Conference on Probability Theory (Braçsov, 1979), pages 205–219, Bucharest, 1981. Ed. Acad. R.S. Romania.ˆ [3367] Jack Schechtman. An income fluctuation problem. J. Econ. Theory 12, 218-241, 1976. [3368] V. Scheiber. Versuchsplaene zur stochastischen Optimierung. Computing 9, 383-399, 1972. [3369] Klaus Reiner Schenk-Hoppe.´ Random dynamical systems in economics. Stoch. Dyn., 1(1):63–83, 2001. [3370] Kenneth Schilling. Random knapsacks with many constraints. Discrete Appl. Math. 48, No.2, 163-174, 1994. [3371] Kenneth E. Schilling. The growth of m-constraint random knapsacks. Eur. J. Oper. Res. 46, No.1, 109-112, 1990. [3372] L. Schmetterer. uber¨ ein rekursives Verfahren von Herrn Hiriart-Urruty. Osterreich.¨ Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, 189(4-7):139–147, 1980. [3373] Leopold Schmetterer. From stochastic approximation to the stochastic theory of optimization. Ber. Math.-Statist. Sekt. Forsch. Graz, 124-132:Ber. No. 127, 40, 1979. Eleventh Styrian Mathematical Symposium (Graz, 1979).

189 [3374] Leopold Schmetterer. Ueber convexe Programme mit stochastischen Stoerungen. (On convex programs with stochastic perturbations). Nova Acta Leopold., Neue Folge 61, No.267, 85-88, 1989. [3375] R. Schmidt. Optimale Wertpapiermischungen mit Hilfe des Chance-Constrained Programming. In Proc. Oper. Res. 4, DGOR Ann. Meet., Wuerzburg 1974, 51-71, 1974. [3376] Lothar M. Schmitt. Theory of genetic algorithms. Theoret. Comput. Sci., 259(1-2):1–61, 2001. [3377] S. Schmuntzsch. Beruecksichtigung der Ertragsunsicherheit in Optimierungsmodellen der Pﬂanzenproduktion. Biometr. Z. 15, 301-312, 1973. [3378] A.H. Schneeweiss. Entscheidungskriterien bei Risiko. Springer, Berlin, 1967. (in German). [3379] Ch. Schneeweiss. Ueber den Zusammenhang von quadratischer stochastischer dynamischer Pro- grammierung und Wiener-Newton Theorie. In Operations Res.-Verf. 13, IV. Oberwolfach-Tag. Operations Res. 1971, 367- 379, 1972. [3380] Ch. Schneeweiss. Zur Theilschen Theorie dynamischer Sicherheitsaequivalente. In Proc. Oper. Res., DGU Ann. Meet. 1971, 177-188, 1972. [3381] Christoph Schneeweiss. Optimale Prognosen und sufﬁziente Statistiken in quadratischen dynamischen Optimierungsproblemen. Statist. Hefte, n. F. 13, 116-129, 1972. [3382] Christoph Schneeweiss. Dynamisches Programmieren. Physica Paperback. Wuerzburg - Wien: Physica-Verlag., 1974. [3383] Christoph Schneeweiss. Elemente einer Theorie hierarchischer Planung. OR Spektrum 16, No.2, 161-168, 1994. [3384] Wolfgang Schneiderheinze. Numerically stable solution of linear least squares problems. In Nu- merical methods of nonlinear programming and their implementations (Quedlinburg, 1989), volume 60 of Math. Res., pages 127–144. Akademie-Verlag, Berlin, 1991. [3385] Fabio Schoen. Stochastic techniques for global optimization: a survey of recent advances. J. Global Optim., 1(3):207–228, 1991. [3386] Fabio Schoen. On a new stochastic global optimization algorithm based on censored observations. J. Global Optim., 4(1):17–35, 1994. [3387] R. Schultz. Rates of convergence in stochastic programs with complete integer recourse. Re- port 483, Schwerpunktprogramm der Deutschen Forschungsgemeinschaft ‘Anwendungsbezogene Optimierung und Steuerung’, 1993. [3388] R. Schultz. Discontinuous optimization problems in stochastic integer programming. Preprint SC 95-20, Konrad-Zuse-Zentrum fur¨ Informationstechnik Berlin, 1995. [3389] R. Schultz. On structure and stability in stochastic programs with random technology matrix and complete integer recourse. Mathematical Programming, 70:73–89, 1995. [3390] R. Schultz. Rates of convergence in stochastic programs with complete integer recourse. SIAM Journal on Optimization, 6(4):1138–1152, 1996. [3391] R. Schultz, L. Stougie, and M.H. van der Vlerk. Two-stage stochastic integer programming: a survey. Statist. Neerlandica, 50(3):404–416, 1996. [3392] Rudiger¨ Schultz. Some consequences of optimal-value-sensitivity for sensitivity of optimal solutions in stochastic linear programming with recourse. In 17. Jahrestagung “Mathematische Opti- mierung” (Rostock, 1986), volume 85 of Seminarberichte, pages 118–127. Humboldt Univ. Berlin, 1986.

190 [3393] Rudiger¨ Schultz. Continuity properties of expectation functions in stochastic integer programming. Math. Oper. Res., 18(3):578–589, 1993. [3394] Rudiger¨ Schultz. Strong convexity in stochastic programs with complete recourse. J. Comput. Appl. Math., 56(1-2):3–22, 1994. Stochastic programming: stability, numerical methods and applications (Gosen, 1992). [3395] Rudiger¨ Schultz. On structure and stability in stochastic programs with random technology matrix and complete integer recourse. Math. Programming, 70(1, Ser. A):73–89, 1995. [3396] Rudiger¨ Schultz. A note on preprocessing via Fourier-Motzkin elimination in two-stage stochastic programming. In Stochastic programming methods and technical applications (Neubiberg/Munich, 1996), pages 208–222. Springer, Berlin, 1998. [3397] Rudiger¨ Schultz. Some aspects of stability in stochastic programming. Ann. Oper Res., 100:55–84 (2001), 2000. Research in stochastic programming (Vancouver, BC, 1998). [3398] Rudiger¨ Schultz, Leen Stougie, and Maarten H. van der Vlerk. Solving stochastic programs with integer recourse by enumeration: a framework using Grobner¨ basis reductions. Math. Program- ming, 83(2, Ser. A):229–252, 1998. [3399] Rudiger¨ Schultz and Stephan Tiedemann. Risk aversion via excess probabilities in stochastic programs with mixed-integer recourse. Stochastic Programming E-Print Series, http://www. speps.org, 2002. [3400] Rudiger¨ Schultz and Stephan Tiedemann. Conditional value-at-risk in stochastic programs with mixed-integer recourse. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [3401] Rudiger¨ Schultz and Stephan Tiedemann. Conditional value-at-risk in stochastic programs with mixed-integer recourse. Math. Program., 105(2-3, Ser. B):365–386, 2006. [3402] Ruediger Schultz. Continuity and stability in two-stage stochastic integer programming. In Stochastic optimization. Numerical methods and technical applications, Proc. GAMM/IFIP- Workshop, Neubiberg/Ger. 1990, Lect. Notes Econ. Math. Syst. 379, 81-92, 1992. [3403] Andreas S. Schulz. New Old Algorithms for Stochastic Scheduling. In S. Albers, R.H. Mohring,¨ G.Ch. Pﬂug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [3404] Peter Schutz,¨ Leen Stougie, and Asgeir Tomasgard. Facility location with uncertain demand and economies of scale. In S. Albers, R.H. Mohring,¨ G.Ch. Pﬂug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http: //www.dagstuhl.de/05031, 2005. [3405] Gideon Schwarz. Game theory and statistics. In Handbook of game theory with economic applications, Vol. II, volume 11 of Handbooks in Econom., pages 769–779. North-Holland, Amsterdam, 1994. [3406] Eithan Schweitzer. An interior random vector algorithm for multistage stochastic linear programs. SIAM J. Optim., 8(4):956–972 (electronic), 1998. [3407] Eithan Schweitzer and Mordecai Avriel. A Gaussian upper bound for Gaussian multi-stage stochastic linear programs. Math. Programming (Ser. A), 77(1):1–21, 1997. [3408] Rudolf Scitovski. An approach in solving nonlinear least squares problems. In IV conference on applied mathematics (Split, 1984), pages 109–113. Univ. Split, Split, 1985. [3409] C.H. Scott and T.R. Jefferson. Convex stochastic programmes with simple recourse. Int. J. Systems Sci. 10, 1143-1148, 1979.

191 [3410] C.H. Scott and T.R. Jefferson. Zero degree of difficulty programs and the distribution problem. Int. J. Syst. Sci. 11, 129-138, 1980. [3411] T. J. Scott and E. G. Read. Modelling hydro reservoir operation in a deregulated electricity sector. International Transactions in Operations Research, 3(3-4):209–221, 1996. [3412] D. Sculli. A stochastic cutting stock procedure: Cutting rolls of insulating tape. Manage. Sci. 27, 946-952, 1981. [3413] Hans-Juergen Sebastian. Dynamische Optimierung unter Einbeziehung zeitabhaengiger Ein- flussparameter. Math. Operationsforsch. Statistik 7, 427-452, 1976. [3414] Hans-Juergen Sebastian. Eine erweiterte Bellmannsche Funktionalgleichung der dynamischen Op- timierung. Math. Operationsforsch. Stat., Optimization 8, 509-527, 1977. [3415] Giovanni Sebastiani and Giovanni Luca Torrisi. An extended ant colony algorithm and its convergence analysis. Methodol. Comput. Appl. Probab., 7(2):249–263, 2005. [3416] E.V. Sedunov. Numerical methods for optimal unbiased design of an experiment in a Hilbert space. Kibernetika (Kiev), 5:55–62, 134, 1988. [3417] R.S. Segall. Some deterministic and stochastic nonlinear optimization modelling for the spatial allocation of multicategorical resources: with an application to real health data. Appl. Math. Mod- elling 13, No.11, 641-650, 1989. [3418] W. Seidel. An open optimization problem in statistical quality control. J. Global Optim., 1(3):295– 303, 1991. [3419] Abraham Seidmann. Optimal dynamic routing in flexible manufacturing systems with limited buffers. Ann. Oper. Res. 15, 291-311, 1988. [3420] M.P. Semesenko. Random processes in control systems. (Sluchajnye protsessy v sistemakh upravleniya). Kiev-Donetsk: Vishcha Shkola. 192 p. R. 1.60, 1986. [3421] S. Sen, R.D. Doverspike, and S. Cosares. Network planning with random demand. Telecommuni- cation Systems 3:11-30, 1994. [3422] Suvrajeet Sen. Relaxations for probabilistically constrained programs with discrete random variables. In System modelling and optimization (Zurich, 1991), volume 180 of Lecture Notes in Control and Inform. Sci., pages 598–607. Springer, Berlin, 1992. [3423] Suvrajeet Sen. Relaxations for probabilistically constrained programs with discrete random variables. Oper. Res. Lett., 11(2):81–86, 1992. [3424] Suvrajeet Sen. Subgradient decomposition and differentiability of the recourse function of a two- stage stochastic linear program. Oper. Res. Lett., 13(3):143–148, 1993. [3425] Suvrajeet Sen and Julia L. Higle. An Introductory Tutorial on Stochastic Linear Programming Models. Interfaces, 29(2):33–61, 1999. [3426] Suvrajeet Sen and Julia L. Higle. The c3 theorem and a d2 algorithm for large scale stochastic integer programming: Set convexification. Stochastic Programming E-Print Series, http:// www.speps.org, 2000. [3427] Suvrajeet Sen and Julia L. Higle. The C3 theorem and a D2 algorithm for large scale stochastic mixed-integer programming: set convexification. Math. Program., 104(1, Ser. A):1–20, 2005. [3428] Suvrajeet Sen, Julia L. Higle, and John R. Birge. Duality gaps in stochastic integer programming. J. Global Optim., 18(2):189–194, 2000.

192 [3429] Suvrajeet Sen, Jason Mai, and Julia L. Higle. Solution of large scale stochastic programs with stochastic decomposition algorithms. In Large scale optimization (Gainesville, FL, 1993), pages 388–410. Kluwer Acad. Publ., Dordrecht, 1994. [3430] Suvrajeet Sen, Lihua Yu, and Talat Genc. A stochastic programming approach to power portfolio optimization. Oper. Res., 54(1):55–72, 2006. [3431] Jati K. Sengupta. Chance-constrained linear programming with chi-square type deviates. Manage- ment Sci., 19(3):337–349, 1972. [3432] Jati K. Sengupta. Stochastic programming. North-Holland Publishing Co., Amsterdam, 1972. Methods and applications. [3433] Jati K. Sengupta. An iterative convex simplex method for geometric programming with applications. Internat. J. Systems Sci., 8(1):49–63, 1977. [3434] Jati K. Sengupta. Adaptive decision rules for stochastic linear programming. Internat. J. Systems Sci., 9(1):97–109, 1978. [3435] Jati K. Sengupta. Bilinear models in stochastic programming. J. Cybernet., 9(2):161–168, 1979. [3436] Jati K. Sengupta. A class of bilinear models in stochastic programming with applications. Internat. J. Systems Sci., 10(3):307–320, 1979. [3437] Jati K. Sengupta. Complementarity theorems in stochastic programming. Internat. J. Systems Sci., 10(10):1081–1095, 1979. [3438] Jati K. Sengupta. Stochastic goal programming with estimated parameters. Z. Nationalokonom.¨ , 39(3-4):225–243, 1979. [3439] Jati K. Sengupta. Testing and validation problems in stochastic linear programming. J. Cybernet., 9(1):17–42, 1979. [3440] Jati K. Sengupta. Linear allocation rules under uncertainty. Int. J. Syst. Sci. 11, 1459-1480, 1980. [3441] Jati K. Sengupta. Minimax solutions in stochastic programming. Cybernet. Systems, 11(1-2):1–19, 1980. [3442] Jati K. Sengupta. Selecting an optimal solution in stochastic linear programming. Internat. J. Systems Sci., 11(1):33–47, 1980. [3443] Jati K. Sengupta. Stochastic programming: a selective survey of recent economic applications. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 525–536. Academic Press, London, 1980. [3444] Jati K. Sengupta. Stochastic programs as non-zero sum games. Internat. J. Systems Sci., 11(10):1145–1162, 1980. [3445] Jati K. Sengupta. Decision models in stochastic programming, volume 7 of North-Holland Series in System Science and Engineering. North-Holland Publishing Co., New York, 1981. Operational methods of decision making under uncertainty. [3446] Jati K. Sengupta. Optimal decisions under uncertainty, volume 193 of Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin, 1981. [3447] Jati K. Sengupta. A minimax policy for optimal portfolio choice. Int. J. Syst. Sci. 13, 39-56, 1982. [3448] Jati K. Sengupta. The active approach of stochastic optimization with new applications. In Econo- metrics of planning and efﬁciency, Vol. dedic. Mem. G. Tintner, Adv. Stud. Theor. Appl. Econ. 11, 93-108, 1988.

193 [3449] Jati K. Sengupta. Nonparametric tests of efficiency of portfolio investment. Z. Nationalokonom.¨ , 50(1):1–15, 1989. [3450] Jati K. Sengupta. Robust solutions in stochastic linear programming. J. Oper. Res. Soc. 42, No.10, 857-870, 1991. [3451] Jati K. Sengupta. The influence curve approach in data envelopment analysis. Math. Program., Ser. B 52, No.1, 147-166, 1991. [3452] Jati K. Sengupta. Nonparametric approach to stochastic linear programming. Internat. J. Systems Sci., 24(5):857–871, 1993. [3453] Jati K. Sengupta and Raymond E. Sfeir. Minimax method of measuring productive efficiency. Int. J. Syst. Sci. 19, No.6, 889-904, 1988. [3454] J.K. Sengupta. A generalization of some distribution aspects of chance-constrained linear programming. Int. Econ. Rev. 11, 287-304, 1970. [3455] J.K. Sengupta. Stochastic linear programming with chance constraints. Int. Econ. Rev. 11, 101-116, 1970. [3456] J.K. Sengupta. A system reliability approach to linear programming. Unternehmensforsch. 15, 112-129, 1971. [3457] J.K. Sengupta. A statistical reliability approach to linear programming. Unternehmensforschung, 15:255–278, 1971. [3458] J.K. Sengupta. Fractile programming under extreme value distributions for the stochastic objective function. J. Cybernet., 2(2):48–60, 1972. [3459] J.K. Sengupta. Application of system reliability measures in chance-constrained programming. Cahiers Centre Etud. Rech. oper. 15, 449-473, 1973. [3460] J.K. Sengupta. Estimating parameters of a linear programming model. J. Cybernet., 6(3-4):309– 328, 1976. [3461] J.K. Sengupta. Adaptive stochastic programming models in economic systems. In Proceedings of the First International Conference on Mathematical Modeling (St. Louis, Mo., 1977), Vol. V, pages 196–206, Rolla, Mo., 1977. Univ. Missouri-Rolla. [3462] J.K. Sengupta and G. Tintner. A review of stochastic linear programming. Rev. Inst. Int. Stat. 39, 197-223, 1971. [3463] Sailes K. Sengupta. Lower semicontinuous stochastic games with imperfect information. Ann. of Statist. 3, 554-558, 1975. [3464] Linn I. Sennott. A new condition for the existence of optimal stationary policies in average cost Markov decision processes. Oper. Res. Lett. 5, 17-23, 1986. [3465] Linn I. Sennott. Computing average optimal constrained policies in stochastic dynamic programming. Probab. Engrg. Inform. Sci., 15(1):103–133, 2001. [3466] Y. Seppaelae. A stochastic multigoal investment model for the public sector. In Prog. Oper. Res., Eger 1974, Colloq. Math. Soc. Janos Bolyai 12, 845-863 , 1976. [3467] Yrjoe Seppaelae. On accurate linear approximations for chance-constrained programming. J. Oper. Res. Soc. 39, No.7, 693-694, 1988. [3468] Yrjoe Seppaelae and Tuomo Orpana. Experimental study on the efficiency and accuracy of a chance-constrained programming algorithm. Eur. J. Oper. Res. 16, 345-357, 1984.

194 [3469] Yrjo¨ Seppal¨ a.¨ Constructing sets of uniformly tighter linear approximations for a chance constraint. Management Sci., 17:736–749, 1970/71. [3470] Yrjo¨ Seppal¨ a.¨ A chance-constrained programming algorithm. Nordisk Tidskr. Informationsbehan- dling (BIT), 12:376–399, 1972. [3471] I.V. Sergienko and V.P. Shilo. Probabilistic decomposition of integer linear programming problems with Boolean variables, and the automatic choice of algorithms for their solution. Kibernet. Sistem. Anal., 2:149–158, 191, 1994. [3472] G.N. Serikov. A differential game with an integral plateau. Differential Equations 1 994-999 (1976)., 1974. [3473] S. P. Sethi, H. Yan, and H. Zhang. Peeling layers of an onion: inventory model with multiple delivery modes and forecast updates. J. Optim. Theory Appl., 108(2):253–281, 2001. [3474] S.P. Sethi and C. Bes. Dynamic stochastic optimization problems in the framework of forecast and decision horizons. In Advances in optimization and control (Montreal, PQ, 1986), volume 302 of Lecture Notes in Econom. and Math. Systems, pages 230–246. Springer, Berlin, 1988. [3475] S.P. Sethi, W. Suo, M.I. Taksar, and Q. Zhang. Optimal production planning in a stochastic manufacturing system with long-run average cost. J. Optim. Theory Appl., 92(1):161–188, 1997. [3476] Jiri Sgall. Online Scheduling. In S. Albers, R.H. Mohring,¨ G.Ch. Pﬂug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http:// www.dagstuhl.de/05031, 2005. [3477] Eli Shamir. Remarks on the stochastic travelling salesman. In Random graphs, Vol. 2 (Poznan,´ 1989), Wiley-Intersci. Publ., pages 233–236. Wiley, New York, 1992. [3478] Ron Shamir. Probabilistic analysis in linear programming. In Probability and algorithms, pages 131–148. Nat. Acad. Press, Washington, DC, 1992. [3479] A. Shapiro. Stochastic programming with equilibrium constraints. J. Optim. Theory Appl., 128(1):223–243, 2006. [3480] A. Shapiro and Y. Wardi. Convergence analysis of gradient descent stochastic algorithms. J. Optim. Theory Appl., 91(2):439–454, 1996. [3481] A. Shapiro and Y. Wardi. Convergence analysis of stochastic algorithms. Math. Oper. Res., 21(3):615–628, 1996. [3482] Alexander Shapiro. Asymptotic properties of statistical estimators in stochastic programming. Ann. Statist., 17(2):841–858, 1989. [3483] Alexander Shapiro. On differential stability in stochastic programming. Math. Programming, 47(1 (Ser. A)):107–116, 1990. [3484] Alexander Shapiro. Asymptotic analysis of stochastic programs. Ann. Oper. Res., 30(1-4):169–186, 1991. Stochastic programming, Part I (Ann Arbor, MI, 1989). [3485] Alexander Shapiro. Asymptotic behavior of optimal solutions in stochastic programming. Math. Oper. Res., 18(4):829–845, 1993. [3486] Alexander Shapiro. Quantitative stability in stochastic programming. Math. Programming, 67(1, Ser. A):99–108, 1994. [3487] Alexander Shapiro. Simulation-based optimization—convergence analysis and statistical inference. Comm. Statist. Stochastic Models, 12(3):425–454, 1996.

195 [3488] Alexander Shapiro. Statistical inference of stochastic optimization problems. In Probabilistic constrained optimization, volume 49 of Nonconvex Optim. Appl., pages 282–307. Kluwer Acad. Publ., Dordrecht, 2000. [3489] Alexander Shapiro. Stochastic programming by monte carlo simulation methods. Stochastic Pro- gramming E-Print Series, http://www.speps.org, 2000. [3490] Alexander Shapiro. Statistical inference of multistage stochastic programming problems. Opti- mization Online, http://www.optimization-online.org, 2002. [3491] Alexander Shapiro. Asymptotics of minimax stochastic programs. Optimization Online, http: //www.optimization-online.org, 2006. [3492] Alexander Shapiro. On complexity of multistage stochastic programs. Oper. Res. Lett., 34(1):1–8, 2006. [3493] Alexander Shapiro. Stochastic programming approach to optimization under uncertainty. Opti- mization Online, http://www.optimization-online.org, 2006. [3494] Alexander Shapiro. Worst-case distribution analysis of stochastic programs. Math. Program., 107(1-2, Ser. B):91–96, 2006. [3495] Alexander Shapiro and Shabbir Ahmed. On a class of minimax stochastic programs. SIAM J. Optim., 14(4):1237–1249 (electronic), 2004. [3496] Alexander Shapiro and Tito Homem-de Mello. A simulation-based approach to two-stage stochastic programming with recourse. Math. Programming, 81(3, Ser. A):301–325, 1998. [3497] Alexander Shapiro and Tito Homem-de-Mello. On rate of convergence of optimal solutions of Monte Carlo approximations of stochastic programs. Stochastic Programming E-Print Series, http://www.speps.org, 1999. [3498] Alexander Shapiro and Tito Homem-de Mello. On the rate of convergence of optimal solutions of Monte Carlo approximations of stochastic programs. SIAM J. Optim., 11(1):70–86 (electronic), 2000. [3499] Alexander Shapiro, Tito Homem-de Mello, and Joocheol Kim. Conditioning of convex piecewise linear stochastic programs. Math. Program., 94(1, Ser. A):1–19, 2002. [3500] Alexander Shapiro, Joocheol Kim, and Tito Homem-de-Mello. Conditioning of stochastic programs. Stochastic Programming E-Print Series, http://www.speps.org, 2000. [3501] Alexander Shapiro and Anton Kleywegt. Minimax analysis of stochastic problems. Optim. Meth- ods Softw., 17(3):523–542, 2002. Stochastic programming. [3502] Alexander Shapiro and Arkadi Nemirovski. On complexity of stochastic programming problems. In Continuous optimization, volume 99 of Appl. Optim., pages 111–146. Springer, New York, 2005. [3503] Alexander Shapiro and Huifu Xu. Uniform laws of large numbers for set-valued mappings and subdifferentials of random functions. Optimization Online, http://www. optimization-online.org, 2005. [3504] John J. Shaw, Ronald M. James, and Daniel B. Grunberg. Birth of a salesman. J. Guid. Control Dyn. 11, No.5, 415-420, 1988. [3505] Yosef Shefﬁ and Warren B. Powell. Equivalent minimization programs and solution algorithms for stochastic equilibrium transportation network problems. In Combinatorics, graph theory and computing, Proc. 11th southeast. Conf., Boca Raton/Florida 1980, Vol. I, Congr. Numerantium 28, 81-115, 1980.

196 [3506] Yosef Sheffi and Warren B. Powell. An algorithm for the equilibrium assignment problem with random link times. Networks 12, 191-207, 1982. [3507] Ronald W. Shephard, Rokaya A. Al-Ayat, and Robert C. Leachman. Shipbuilding production function: An example of a dynamic production function. In Quant. Wirtsch.-Forsch., W. Krelle zum 60. Geb., 627-654, 1977. [3508] Hanif D. Sherali and Barbara M. P. Fraticelli. A modification of Benders’ decomposition algorithm for discrete subproblems: an approach for stochastic programs with integer recourse. J. Global Optim., 22(1-4):319–342, 2002. Dedicated to Professor Reiner Horst on his 60th birthday. [3509] H.D. Sherali, A.L. Soyster, F.H. Murphy, and S. Sen. Allocation of capital costs in electric utility capacity expansion planning under uncertainty. Management Science 30:1-19, 1984. [3510] V. R. Sherkat, R. Campo, K. Moslehi, and E. O. Lo. Stochastic long-term hydrothermal optimization for a multireservoir system. IEEE Trans. Power Apparatus and Systems, 104(8):2040–2049, 1985. [3511] Theodore J. Sheskin. Sequencing of diagnostic tests for fault isolation by dynamic programming. IEEE Trans. Reliab. R-27, 353-359, 1978. [3512] Ding-hua Shi and Jian-ping Peng. A new theoretical framework for analyzing stochastic global optimization algorithms. J. Shanghai Univ., 3(3):175–180, 1999. [3513] Hong Yan Shi, Zhi Fei Chen, and Chang Zhi Sun. On the convergence of a hybrid optimization algorithm. Control Decis., 19(5):546–549, 553, 2004. [3514] Leyuan Shi and Sigurdur Olafsson.´ Nested partitions method for stochastic optimization. Methodol. Comput. Appl. Probab., 2(3):271–291, 2000. [3515] Leyuan Shi and Sigurdur Olafsson.´ Stopping rules for the stochastic nested partitions method. Methodol. Comput. Appl. Probab., 2(1):37–58, 2000. [3516] Xiao Fa Shi and Jin De Wang. Approximate Lagrange multiplier algorithm for stochastic programs with complete recourse: nonlinear deterministic constraints. Acta Math. Appl. Sinica (English Ser.), 8(3):207–213, 1992. [3517] S.V. Shibaev. A stochastic algorithm for finding a maximin. In Mathematical methods for the analysis of complex stochastic systems (Russian), pages 12–17, i–ii. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1988. [3518] S.V.Shibaev. A method for finding the minimax of functionals that depend on probability measures. Kibernet. Sistem. Anal., 2:79–85, 189, 1992. [3519] S.V. Shibaev. On finding maximin under marginal constraints. Kibernet. Sistem. Anal., 6:103–114, 186, 1994. [3520] Wei Shih. Joint determination of pricings, productions and budget allocations with a chance- constrained approach. Int. J. Inf. Manage. Sci. 5, No.2, 41-52, 1994. [3521] T. Shiina. Numerical solution technique for joint chance-constrained programming problem –an application to electric power capacity expansion–. Journal of the Operations Research Society of Japan, 42:128–140, 1999. [3522] T. Shiina. L–shaped decomposition method for multi-stage stochastic concentrator location problem. Journal of the Operations Research Society of Japan, 43:317–332, 2000. [3523] Takayuki Shiina. L-shaped method for stochastic integer programming problem. Surikaisekikenky¯ usho¯ Koky¯ uroku¯ , (1132):154–164, 2000. Mathematical decision theory under uncertainty and ambiguity (Japanese) (Kyoto, 1999).

197 [3524] Takayuki Shiina and John R. Birge. Stochastic unit commitment problem. Surikaisekikenky¯ usho¯ Koky¯ uroku¯ , (1252):117–123, 2002. Mathematical decision making under uncertainty (Japanese) (Kyoto, 2001). [3525] Takayuki Shiina and John R. Birge. Stochastic unit commitment problem. Int. Trans. Oper. Res., 11(1):19–32, 2004. [3526] V. A. Shikhovtsev. The recursive minimization method in problems of the optimization of dynamical systems under uncertainty. Izv. Akad. Nauk Teor. Sist. Upr., (1):40–57, 1999. [3527] S.V. Shil’man. Stochastic approximation in filtering and identification problems. Eng. Cybern. 21, No.4, 77-84 translation from Izv. Akad. Nauk SSSR, Tekh. Kibern. 1983, No.4, 86-94 (1983)., 1983. [3528] S.V. Shil’man. A stochastic quasigradient method for quadratic optimization under dependent observations. Avtomat. i Telemekh., 12:70–80, 1992. [3529] S.V. Shil’man and A.I. Yastrebov. Stochastic optimization algorithms with Markov noise in gradient measurements. Autom. Remote Control 41, 817-821 translation from Avtom. Telemekh. 1980, No.6, 96-100 (1980)., 1980. [3530] V. P. Shilo. A method of global equilibrium search. Kibernet. Sistem. Anal., (1):74–81, 190, 1999. [3531] V. P. Shilo. RESTART distributions and an asymptotically exact random algorithm for solving discrete optimization problems. Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki, (2):85– 88, 2001. [3532] V. P. Shilo. Sorting algorithms for solving discrete optimization problems and RESTART distributions. Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki, (1):79–83, 2001. [3533] V.P. Shilo. Application of stochastic programming methods in diffusion process control problems. Cybernetics 14, 741-745 translation from Kibernetika 1978, No.5, 92-95 (1978)., 1979. [3534] V.P. Shilo. Application of stochastic programming methods in problems of optimizing systems described by elliptic equations. In Probabilistic methods in cybernetics, volume 69 of Preprint 79, pages 12–20, 73. Akad. Nauk Ukrain. SSR Inst. Kibernet., Kiev, 1979. [3535] Takashi Shima. Global optimization by generalized random tunneling algorithm and its application to system identification and control problems using neural networks. Trans. Inst. Systems Control Inform. Engrs., 7(3):84–93, 1994. [3536] T. Shimizu. A stochastic approximation method for optimization problems. J. Assoc. Comput. Mach. 16, 511-516, 1969. [3537] Nahum Shimkin. Extremal large deviations in controlled i.i.d. processes with applications to hypothesis testing. Adv. in Appl. Probab., 25(4):875–894, 1993. [3538] S. Shiode, H. Ishii, and T. Nishida. Errata: “A stochastic linear knapsack problem” [Naval Res. Logist. 34 (1987), no. 5, 753–759; MR 88h:90158]. Naval Res. Logist., 37(4):600, 1990. [3539] Shogo Shiode and Hiroaki Ishii. A single facility stochastic location problem under A-distance. Ann. Oper. Res. 31, 469-478, 1991. [3540] Shogo¯ Shiode, Hiroaki Ishii, and Toshio Nishida. A chance constrained minimax facility location problem. Math. Japon., 30(5):783–803, 1985. [3541] Shogo¯ Shiode, Hiroaki Ishii, and Toshio Nishida. A stochastic linear knapsack problem. Naval Res. Logist., 34(5):753–759, 1987. [3542] A.V. Shirin. On an algorithm for the estimation of parameters of linear regression equations by the method of random improving. Probl. Sluchajnogo Poiska 8, 275-279, 1980.

198 [3543] David B. Shmoys and Chaitanya Swamy. An approximation scheme for stochastic linear programming and its application to stochastic integer programs. J. ACM, 53(6):978–1012 (electronic), 2006. [3544] E.I. Shor. Optimal control of an object with a multiplicative continuously distributed unknown parameter. Kibernetika 1982, No.1, 121-122, 1982. [3545] N. Z. Shor, T. A. Bardadym, N. G. Zhurbenko, A. P. Likhovid, and P. I. Stetsyuk. Application of nonsmooth optimization methods in stochastic programming problems. Kibernet. Sistem. Anal., (5):33–47, 188, 1999. [3546] Eugene Shragowitz and Rung-Bin Lin. Combinatorial optimization, Markov chains, and stochastic automata. In Numerical solution of Markov chains, volume 8 of Probab. Pure Appl., pages 543– 564. Dekker, New York, 1991. [3547] A.K. Shukla and S.N. Gupta. A stochastic linear programming approach for crop planning. Acta Cienc. Indica, Math. 15, No.3, 265-270, 1989. [3548] A.K. Shukla and S.N. Gupta. A stochastic model for minimizing variability. Acta Cienc. Indica, Math. 15, No.3, 259-264, 1989. [3549] Andrzej Sierocinski´ and Jerzy Zabczyk. On a packing problem. In Stochastic systems and optimization (Warsaw, 1988), volume 136 of Lecture Notes in Control and Inform. Sci., pages 356–359. Springer, Berlin, 1989. [3550] C.E. Sigal, A.A.B. Pritsker, and J.J. Solberg. The use of cutsets in Monte Carlo analysis of stochastic networks. Math. Comput. Simulation, 21(4):376–384, 1979. [3551] C.Elliott Sigal, A.Alan B. Pritsker, and James J. Solberg. The stochastic shortest route problem. Oper. Res. 28, 1122-1129, 1980. [3552] Wojciech Sikora. Transportation problem with random demand. Przegl. Stat. 39, No.3-4, 351-364, 1992. [3553] K.A. Sikorski and A. Borkowski. Ultimate load analysis by stochastic programming. In Smith, D. Lloyd (ed.): Mathematical programming methods in structural plasticity. Wien etc.: Springer- Verlag (ISBN 3-211-82191-0). CISM Courses Lect. 299, 403-424, 1990. [3554] V.P. Silo.ˇ Elliptic equations and boundary control. In Methods in operations research and reliability theory in systems of analysis (Russian), pages 76–80, 102, Kiev, 1979. Akad. Nauk Ukrain. SSR Inst. Kibernet. [3555] Eduardo F. Silva and R. Kevin Wood. Solving a class of stochastic mixed-integer programs with branch and price. Math. Program., 108(2-3, Ser. B):395–418, 2006. [3556] Thomas M. Simundich. An efﬁcient algorithm for solving a stochastic, integer programming problem arising in radio navigation. In Optim. Techn., Proc. IFIP Conf., Wuerzburg 1977, Part 2, Lect. Notes Control Inf. Sci. 7, 263-268, 1978. [3557] Diptendu Sinha and Jerry C. Wei. Stochastic analysis of ﬂexible process choices. Eur. J. Oper. Res. 60, No.2, 183-199, 1992. [3558] Hans-Werner Sinn. Economic decisions under uncertainty. Transl. from the German. 2nd ed., 1989. [3559] K. Sirlantzis, J. D. Lamb, and W. B. Liu. Novel algorithms for noisy minimization problems with applications to neural networks training. J. Optim. Theory Appl., 129(2):325–340, 2006. [3560] Stergios Skaperdas. Contest success functions. Econom. Theory, 7(2):283–290, 1996.

199 [3561] Karel Sladky.´ On a multistage stochastic linear program. In Asymptotic statistics (Prague, 1993), Contrib. Statist., pages 435–446. Physica, Heidelberg, 1994. [3562] R. Slowinski´ and J. Teghem. A comparison study of “STRANGE” and “FLIP”. In Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, volume 6 of Theory Decis. Lib. Ser. D System Theory Knowledge Engrg. Probl. Solving, pages 365–393. Kluwer Acad. Publ., Dordrecht, 1990. [3563] Roman Slowinski. A multicriteria fuzzy linear programming method for water supply system development planning. Fuzzy Sets Syst. 19, 217-237, 1986. [3564] Roman Slowinski´ and Jacques Teghem, editors. Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, volume 6 of Theory and Decision Library. Series D: System Theory, Knowledge Engineering and Problem Solving. Kluwer Academic Pub- lishers Group, Dordrecht, 1990. [3565] Y. Smeers. Traitement de l’incertain dans le calcul des plans d’equipement´ electrique.´ In B. Cor- net and H. Tulkens, editors, Modelisation´ et Decision´ Economique, Bruxelles, 1990. De Boeck Universite.´ [3566] V.V. Smirnova. Inequality systems with random coefficients in linear stochastic programming. Issled. Oper. ASU 20, 49-55, 1982. [3567] V.V. Smirnova. Systems of inequalities with random coefficients in linear stochastic programming. Issled. Operatsii i ASU, 20:49–55, 1982. [3568] Douglas V. Smith. Decision rules in chance-constrained programming: Some experimental comparisons. Management Sci., Appl. 19, 688-702, 1973. [3569] J. Cole Smith, Andrew J. Schaefer, and Joyce W. Yen. A stochastic intra-ring synchronous optimal network design problem. Stochastic Programming E-Print Series, http://www.speps.org, 2002. [3570] J. MacGregor Smith and Nikhil Chikhale. Buffer allocation for a class of nonlinear stochastic knapsack problems. Ann. Oper. Res., 58:323–360, 1995. Applied mathematical programming and modeling, II (APMOD 93) (Budapest, 1993). [3571] James E. Smith and Kevin F. McCardle. Structural properties of stochastic dynamic programs. Oper. Res., 50(5):796–809, 2002. [3572] L.G. Smyshlyaeva. Sufficient conditions for optimizing the dimension of the state vector of a dynamical system. Vestnik Leningrad. Univ. Mat. Mekh. Astronom., 1:42–45, 123, 1989. [3573] Moshe Sniedovich. Preference order stochastic knapsack problems: Methodological issues. J. Oper. Res. Soc. 31, 1025-1032, 1980. [3574] Moshe Sniedovich. Analysis of a preference order traveling salesman problem. Oper. Res. 29, 1234-1237, 1981. [3575] Moshe Sniedovich. Some comments on preference order dynamic programming models. J. Math. Anal. Appl. 79, 489-501, 1981. [3576] Moshe Sniedovich. A class of variance-constrained problems. Oper. Res., 31(2):338–353, 1983. [3577] Moshe Sniedovich. Solution strategies for variance minimization problems. Comput. Math. Appl., 21(2-3):49–56, 1991. [3578] Juan-Miguel Soler Salcedo. A model of cybernetic stochastic economy. Revista Acad. Ci. Madrid 66, 11-16, 1972.

200 [3579] D. P. Solomatine. Two strategies of adaptive cluster covering with descent and their comparison to other algorithms. J. Global Optim., 14(1):55–78, 1999. [3580] J.E. Somers. Maximum flow in networks with a small number of random arc capacities. Networks 12, 241-253, 1982. [3581] Laszlo Somlyody and Roger J.-B. Wets. Stochastic optimization models for lake eutrophication management. Oper. Res. 36, No.5, 660-681, 1988. [3582] J. Song, Y. Xu, Y. Yam, and M.C. Nechyba. Optimization of human control strategy with simultaneous perturbation stochastic approximation. In Proceedings of the IEEE Conference on Intelligent Robots and Systems, Part 2, pages 983–988, 1998. [3583] N.Z. Sorˇ and M.B. Sˇcepakin.ˇ An algorithm for solution of a two step problem of stochastic programming. Kibernetika (Kiev), 3:56–58, 1968. [3584] N.Z. Sorˇ and M.B. Sˇcepakin.ˇ Multistage stochastic programming problems in parametric form. In Theory of optimal solutions (Proc. Sem., Kiev, 1968), No. 3 (Russian), pages 64–73, Kiev, 1969. Akad. Nauk Ukrain. SSR. [3585] Marilda de Oliveira Sotomayor. On income fluctuations and capital gains with a convex production function. J. Econom. Dynamics Control, 11(3):285–312, 1987. [3586] M. Souissi and Y. Smeers. Reliability optimization of complex systems using sharp lower bounds. In System modelling and optimization (Prague, 1995), pages 339–346. Chapman & Hall, London, 1996. [3587] Charles R. Sox. Dynamic lot sizing with random demand and non-stationary costs. Oper. Res. Lett., 20(4):155–164, 1997. [3588] A.L. Soyster, R.D. Foley, and F.H. Murphy. A class of stochastic mathematical programs with correlated scale parameters in the objective and right-hand side. Oper. Res., 32(4):945–951, 1984. [3589] R. Spaans and R. Luus. Importance of search-domain reduction in random optimization. J. Optim. Theory Appl., 75(3):635–638, 1992. [3590] James C. Spall. A one-measurement form of simultaneous perturbation stochastic approximation. Automatica J. IFAC, 33(1):109–112, 1997. [3591] James C. Spall. Stochastic optimization. In Handbook of computational statistics, pages 169–197. Springer, Berlin, 2004. [3592] J.C. Spall. A stochastic approximation technique for generating maximum likelihood parameter estimates. In Proceedings of the American Control Conference, pages 1161–1167, 1987. [3593] J.C. Spall. Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Transactions on Automatic Control, 37:332–341, 1992. [3594] J.C. Spall. Developments in stochastic optimization algorithms with gradient approximations based on function measurements. In Proceedings of the Winter Simulation Conference, eds. J.D. Tew, M.S. Manivannan, D.A. Sadowski, and A.F. Seila, pages 207–214, 1994. [3595] J.C. Spall. Adaptive stochastic approximation by the simultaneous perturbation method. In Pro- ceedings of the IEEE Conference on Decision and Control, pages 3872–3879, 1998. [3596] J.C. Spall. Implementation of the simultaneous perturbation algorithm for stochastic optimization. IEEE Transactions on Aerospace and Electronic Systems, 34:817–823, 1998. [3597] J.C. Spall. Overview of the simultaneous perturbation method for efficient optimization. http: //techdigest.jhuapl.edu/td/td1904/spall.pdf, Hopkins APL Technical Digest, 19:482–492, 1998.

201 [3598] J.C. Spall. Resampling-based calculation of the information matrix in nonlinear statistical models. In Proceedings of the 4th Joint Conference on Information Sciences, volume 4, pages 35–39, Research Triangle Park, NC, October 1998. [3599] J.C. Spall. Adaptive stochastic approximation by the simultaneous perturbation method. IEEE Transactions on Automatic Control, 45:in press, 2000. [3600] J.C. Spall and J.A. Cristion. Nonlinear adaptive control using neural networks: Estimation based on a smoothed form of simultaneous perturbation gradient approximation. Statistica Sinica, 4:1–27, 1994. [3601] J.C. Spall and J.A. Cristion. A neural network controller for systems with unmodeled dynamics with applications to wastewater treatment. IEEE Transactions on Systems, Man, and Cybernet- ics?B, 27:369–375, 1997. [3602] J.C. Spall and J.A. Cristion. Model-free control of nonlinear stochastic systems with discrete-time measurements. IEEE Transactions on Automatic Control, 43:1198–1210, 1998. [3603] J.C. Spall, S.D. Hill, and D.S. Stark. Some theoretical comparisons of evolutionary computation and other optimization approaches. In Proceedings of the Congress on Evolutionary Computation, pages 1398–1405, Washington, DC, July 1999. [3604] Michael Spence and David Starrett. Most rapid approach paths in accumulation problems. Internat. econom. Review 16, 388-403, 1975. [3605] Georghios P. Sphicas and Fred N. Silverman. Deterministic equivalents for stochastic assembly line balancing. AIIE Trans., 8(2):280–282, 1976. [3606] Liliana Spircu. Distribution of optimum in stochastic linear programming. Econ. Comput. Econ. Cybern. Stud. Res. 1977, No.4, 81-92, 1977. [3607] Wolfgang Stadje. Goal-programming- und Nutzenmodelle fur¨ Entscheidungssituationen mit mehreren Zielen und stochastischen Informationen. In Operations Research Verfahren, 30, pages 166–183. Hain, Meisenheim, 1979. [3608] Wolfgang Stadje. Nutzen- und Goal-Programming-Modelle fuer das Vektormaximumproblem und stochastische Verallgemeinerungen. Oper. Res. Verfahren 34, 289-299, 1979. [3609] Wolfgang Stadje. Availability of an operating system during a given time interval: a dynamic programming approach. Naval Res. Logist., 43(4):589–602, 1996. [3610] I. Stancu-Minasian. The stochastic Chebyshev problem. The distribution function of the optimum. Studii Cerc. Mat. 30, 567-577, 1978. [3611] I. M. Stancu-Minasian, R. Caballero, E. Cerda,´ and M. M. Munoz.˜ The stochastic bottleneck linear programming problem. Top, 7(1):123–143, 1999. [3612] I. M. Stancu-Minasian and Stefan Tigan. Continuous time linear-fractional programming. The minimum-risk approach. RAIRO Oper. Res., 34(4):397–409, 2000. [3613] I.M. Stancu-Minasian. Stochastic programming with multiple objective functions. Econom. Comp. Econom. Cybernet. Stud. Res., 1:49–67, 1974. [3614] I.M. Stancu-Minasian. Note on stochastic programming with several objective functions having the vector c random. Stud. Cerc. Mat., 27(4):453–459, 1975. [3615] I.M. Stancu-Minasian. On the multiple minimum risk problem. I. The case of two objective functions. Stud. Cerc. Mat., 28(5):617–623, 1976. [3616] I.M. Stancu-Minasian. On the problem of Kataoka. Stud. Cerc. Mat., 28(1):95–111, 1976.

202 [3617] I.M. Stancu-Minasian. On the problem of minimum multiple risk. II. The case of r .r > 2/ objective functions. Stud. Cerc. Mat., 28(6):723–734, 1976. [3618] I.M. Stancu-Minasian. On stochastic programming with multiple objective functions. In Proceed- ings of the Fifth Conference on Probability Theory (Bras¸ov, 1974), pages 429–436. Editura Acad. R.S.R., Bucharest, 1977. [3619] I.M. Stancu-Minasian. On the multiple minimum risk problem. Bull. Math. Soc. Sci. Math. R.S. Roumanie (N.S.), 23(71)(4):427–437, 1979. [3620] I.M. Stancu-Minasian. Programarea stocastica cu mai multe func¸tii obiectiv. Editura Academiei Republicii Socialiste Romania,ˆ Bucharest, 1980. With a preface by Marius Iosifescu, With an English summary. [3621] I.M. Stancu-Minasian. Stochastic programming with multiple objective functions. Mathematics and its Applications (East European Series). D. Reidel Publishing Co., Dordrecht, 1984. Translated from the Romanian by Victor Giurgiut¸iu. [3622] I.M. Stancu-Minasian. Overview of different approaches for solving stochastic programming problems with multiple objective functions. In Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, volume 6 of Theory Decis. Lib. Ser. D System The- ory Knowledge Engrg. Probl. Solving, pages 71–101. Kluwer Acad. Publ., Dordrecht, 1990. [3623] I.M. Stancu-Minasian. Stochastic programming with multiple fractile criteria. Rev. Roumaine Math. Pures Appl., 37(10):939–944, 1992. [3624] I.M. Stancu-Minasian and S. Tigan. In Komlosi, Sandor (ed.) et al., Proceedings of the 5th international workshop on generalized convexity held at Janus Pannonius University, Pecs, Hungary, August 31-September 2, 1992. Berlin: Springer-Verlag, (ISBN 3-540-57624-X). Lect. Notes Econ. Math. Syst. 405, 322-333. [3625] I.M. Stancu-Minasian and S¸. T¸igan. The stochastic linear-fractional max-min problem. In Itinerant Seminar on Functional Equations, Approximation and Convexity (Cluj-Napoca, 1987), volume 87 of Preprint, pages 275–280, Cluj, 1987. Univ. “Babes¸-Bolyai”. [3626] I.M. Stancu-Minasian and S. Tigan. On some fractional programming models occurring in minimum-risk problems. In Generalized convexity and fractional programming with economic applications, Proc. Workshop, Pisa/Italy 1988, Lect. Notes Econ. Math. Syst. 345, 295-324, 1990. [3627] I.M. Stancu-Minasian and S¸t. T¸igan. The vectorial minimum-risk problem. In Proceedings of the colloquium on approximation and optimization (Cluj-Napoca, 1985), pages 321–328, Cluj, 1985. Univ. Cluj-Napoca. [3628] I.M. Stancu-Minasian and S¸t. T¸igan. A stochastic approach to some linear fractional goal programming problems. Kybernetika (Prague), 24(2):139–149, 1988. [3629] I.M. Stancu-Minasian and S¸t. T¸igan. Multiobjective mathematical programming with inexact data. In Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, volume 6 of Theory Decis. Lib. Ser. D System Theory Knowledge Engrg. Probl. Solving, pages 395–418. Kluwer Acad. Publ., Dordrecht, 1990. [3630] I.M. Stancu-Minasian and S¸tefan T¸igan. The minimum risk approach to special problems of mathematical programming. The distribution function of the optimal value. Anal. Numer.´ Theor.´ Approx., 13(2):175–187, 1984. [3631] I.M. Stancu-Minasian and M.J. Wets. A research bibliography in stochastic programming, 1955– 1975. Operations Res., 24(6):1078–1119, 1976.

203 [3632] Nikolai Stanulov and Ivailo Velev. Information model for optimum operation planning of the production for an industrial complex. B”lgar. Akad. Nauk., Izv. Inst. tehn. Kibernetika 18, 49-59, 1974. [3633] R.M. Stark. On zero-degree stochastic geometric programs. J. Optimization Theory Appl., 23(1):167–182, 1977. [3634] Scott Stark. Stochastic global optimization applied to reaction network parameter estimation. In Parallel processing for scientific computing (Houston, TX, 1991), pages 180–185. SIAM, Philadel- phia, PA, 1992. [3635] J. R. Stedinger. Stochastic multi-reservoir hydroelectric scheduling. In Proceedings 28. In- ternationales Wasserbau-Symposium, Wasserwirtschafliche Systeme—Konzepte, Konflikte, Kom- promisse, pages 89–117, Aachen, Germany, 1998. Institut fur¨ Wasserbau und Wasserwirtschaft, Rheinisch-Westfalischen¨ Technischen Hochschule Aachen. [3636] J. Michael Steele. Probability and problems in Euclidean combinatorial optimization. In Probabil- ity and algorithms, pages 109–129. Nat. Acad. Press, Washington, DC, 1992. [3637] J.Michael Steele. Probabilistic algorithm for the directed traveling salesman problem. Math. Oper. Res. 11, 343-350, 1986. [3638] Stefan M. Stefanov. On the implementation of stochastic quasigradient methods to some facility location problems. Yugosl. J. Oper. Res., 10(2):235–256, 2000. [3639] Marc Steinbach. Tree-Sparse Modeling and Solution of Multistage Stochastic Programs. In S. Al- bers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [3640] Marc C. Steinbach. Hierarchical sparsity in multistage stochastic programs. In Stochastic optimization: algorithms and applications (Gainesville, FL, 2000), pages 385–410. Kluwer Acad. Publ., Dordrecht, 2001. [3641] Marc C. Steinbach. Markowitz revisited: mean-variance models in financial portfolio analysis. SIAM Rev., 43(1):31–85 (electronic), 2001. [3642] Marc C. Steinbach. Tree-sparse convex programs. Math. Methods Oper. Res., 56(3):347–376, 2002. [3643] Karl-Heinz Stenvers. Stochastische Vektoroptimierung zur Auslegung von Tragwerksstrukturen - Loesungsalgorithmen und Versuchsergebnisse. (Stochastic vector optimization for construction of load-bearing structures - Solution algorithms and experimental results)., 1985. [3644] V.E. Stepanov. Phase transitions in random graphs. Teor. Veroyatn. Primen. 15, 200-216, 1970. [3645] L. Stettner and J. Zabczyk. Stochastic version of a penalty method. In Optimization techniques, Proc. 9th IFIP Conf., Warsaw 1979, Part 1, Lect. Notes Control Inf. Sci. 22, 179-183, 1980. [3646] William R.jun. Stewart and Bruce L. Golden. Stochastic vehicle routing: A comprehensive approach. Eur. J. Oper. Res. 14, 371-385, 1983. [3647] Richard H. Stockbridge. Portfolio optimization in markets having stochastic rates. In Stochastic theory and control (Lawrence, KS, 2001), volume 280 of Lecture Notes in Control and Inform. Sci., pages 447–458. Springer, Berlin, 2002. [3648] Gerald Stockl.¨ A stochastic linear programming approach in topology and material optimization. In Stochastic optimization techniques (Neubiberg/Munich, 2000), volume 513 of Lecture Notes in Econom. and Math. Systems, pages 343–364. Springer, Berlin, 2002.

204 [3649] M. Stoica. Stochastic splitors used in scheduling. Econ. Comput. Econ. Cybern. Stud. Res. 1983, No.1, 63-71, 1983. [3650] L.S. Stoikova and G.N. Sakovich. Sharp upper bounds for a distribution function in a class of unimodal distributions with ﬁxed moments. Dokl. Akad. Nauk Ukrain. SSR Ser. A, 87(1):29–32, 87, 1988. [3651] L.S. Stojkova. Prelimit distribution functions and limit polynomials in a Chebyshev extremal problem. Cybernetics 17, 824-835 translation from Kibernetika 1981, No.6, 95-104 (1981)., 1982. [3652] L.S. Stojkova. On conditions realizing the partitioning of the parameter domain in a Chebyshev extremal problem. Diskretn. Mat. 2, No.4, 11-17, 1990. [3653] Longin Stolc. Stochastic linear programming method for right-hand sides random vector. Internat. J. Systems Sci., 22(7):1197–1208, 1991. [3654] Longin Stolc and Miroslaw Kwiesielewicz. Methods of non-deterministic linear programming in multihorizon system production control. Adv. Modelling Simulation 20, No.3, 33-45, 1990. [3655] L. Stougie. Design and analysis of algorithms for stochastic integer programming, volume 37 of CWI Tract. Stichting Mathematisch Centrum Centrum voor Wiskunde en Informatica, Amsterdam, 1987. [3656] L. Stougie and M.H. van der Vlerk. Stochastic integer programming. In M. Dell’Amico, F. Mafﬁoli, and S. Martello, editors, Annotated Bibliographies in Combinatorial Optimization, chapter 9, pages 127–141. Wiley, 1997. [3657] Leen Stougie and Maarten H. van der Vlerk. Approximation in stochastic integer programming. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [3658] B. Strazicky. On an algorithm for solution of the two-stage stochastic programming problem. In Sechste Oberwolfach-Tagung uber¨ Operations Research (1973), Teil II, pages 142–156. Operations Research Verfahren, Band XIX, Meisenheim am Glan, 1974. Hain. [3659] Beata´ Strazicky. On a method for solving the two-stage stochastic programming problem. Kozlem¨ enyek–MTA´ Szamit´ astechn.´ Automat. Kutato´ Int. Budapest, 11:33–49, 1973. [3660] Beata´ Strazicky. Some results concerning an algorithm for the discrete recourse problem. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 263–274. Aca- demic Press, London, 1980. [3661] L. Streitferdt. Zur Loesung einiger spezieller Verteilungsprobleme der stochastischen Program- mierung. In Proc. Oper. Res. 2, DGOR Ann. Meet. Hamburg 1972, 363-377, 1973. [3662] Simon Streltsov and Pirooz Vakili. A non-myopic utility function for statistical global optimization algorithms. J. Global Optim., 14(3):283–298, 1999. [3663] Peter A. Streufert. Biconvergent stochastic dynamic programming, asymptotic impatience, and “average” growth. J. Econom. Dynam. Control, 20(1-3):385–413, 1996. [3664] Z. Strezova. An approach to the study of complex decision-making systems. In Progr. Cybern. Syst. Res., Vol. IV, Symp. Vienna 1978, 269-277, 1978. [3665] R.G. Strongin. Multi-extremal minimization. Automat. Remote Control, 7:1085–1088, 1970. [3666] R.G. Strongin. Randomization of strategies in the search for a global extremum. In Problems of random search, 2 (Russian), pages 19–29, 219. Izdat. “Zinatne”, Riga, 1973. [3667] R.G. Strongin. Numerical methods in multi-extremal problems (informational-statistical algorithms). (Chislennye metody v mnogoehkstremal’nykh zadachakh (informatsionno-statisticheskie algoritmy)). Moskva: ”Nauka”., 1978.

205 [3668] Cyrille Strugarek. On the fortet-mourier metric for the stability of stochastic optimization problems, an example. Stochastic Programming E-Print Series, http://www.speps.org, 2004. [3669] Gusztavn´ e´ Stubnya. Numerical examples for probabilistic constrained stochastic programming problems. Alkalmaz. Mat. Lapok, 6(3-4):237–255 (1981), 1980. [3670] V.P. Suckov and A.M. Cirlin. Aufgaben der nichtlinearen Programmierung im Mittel und Verteilung von Belastungen zwischen parallelen Aggregaten. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1972, No.3, 17-24, 1972. [3671] Toshiyuki Sueyoshi. Empirical regression quantile. J. Oper. Res. Soc. Japan, 34(3):250–262, 1991. [3672] Yasuo Sugai and Hironori Hirata. Hierarchical algorithm for a partition problem using simulated annealing: application to placement in VLSI layout. Internat. J. Systems Sci., 22(12):2471–2487, 1991. [3673] A.G. Suharev. Ueber optimale Strategien des Suchens eines Extremums. Zh. vycislit. Mat. Mat. Fiz. 11, 910-924, 1971. [3674] De Feng Sun and Jin De Wang. An approximate method for stochastic programming with recourse. Math. Numer. Sinica, 16(1):80–92, 1994. [3675] Jie Sun and Xinwei Liu. Scenario formulation of stochastic linear programs and the homogeneous self-dual interior-point method. INFORMS J. Comput., 18(4):444–454, 2006. [3676] Jie Sun, Kwan Eng Wee, and Jishan Zhu. An interior point method for solving a class of linear- quadratic stochastic programming problems. In Recent advances in nonsmooth optimization, pages 392–404. World Sci. Publishing, River Edge, NJ, 1995. [3677] Jie Sun and Jishan Zhu. A predictor-corrector method for extended linear-quadratic programming. Comput. Oper. Res., 23(8):755–767, 1996. [3678] Shui Ling Sun. A consistency check method for judgment matrices in stratiﬁed analyses. Qufu Shifan Daxue Xuebao Ziran Kexue Ban, 17(3):24–26, 1991. [3679] Zai Dong Sun. A dual algorithm for probabilistic constrained nonlinear programming problems and its convergence. Qufu Shifan Daxue Xuebao Ziran Kexue Ban, 21(5):107–111, 1995. [3680] Sumit Sur and Pradip K. Srimani. Topological properties of star graphs. Comput. Math. Appl. 25, No.12, 87-98, 1993. [3681] D.V. Surnachev. Stochastic analog of Newton’s method. Mosc. Univ. Comput. Math. Cybern. 1982, No.3, 49-53, 1982. [3682] D.V. Surnachev. Stochastic analogue of Newton’s method. Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., 3:40–43, 1982. [3683] Ju. A. Suskov.ˇ A certain way of organizing a random search. In Operations research and statistical modeling, No. 1 (Russian), pages 180–186. Izdat. Leningrad. Univ., Leningrad, 1972. [3684] V.B. Svecinskii.ˇ Random search in probabilistic iterative algorithms. Avtomat. i Telemeh., 1:85–89, 1971. [3685] J.M. Swaminathan and S. R. Tayur. Managing broader product lines through delayed differentiation using vanilla boxes. Working Paper, GSIA, Carnegie Mellon University, Pittsburgh, PA, July 1995, revised March 1996. [3686] Chaitanya Swamy and David Shmoys. Approximation Algorithms for 2-stage and Multi-stage Stochastic Optimization. In S. Albers, R.H. Mohring,¨ G.Ch. Pﬂug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algorithms for Optimization with Incomplete Information, http: //www.dagstuhl.de/05031, 2005.

206 [3687] K. Swarup. On duality in non-linear fractional programming problems. Z. Angew. Math. Mech., 54:734, 1974. [3688] K. Swarup, S.P. Aggarwal, and R.K. Gupta. Stochastic indefinite quadratic programming. Z. Angew. Math. Mech., 52:371–373, 1972. [3689] Arthur J. Swersey and Edward J. Ignall, editors. Delivery of urban services. With a view towards applications in management science and operations research. TIMS Studies in the Management Sciences, Vol. 22. Amsterdam etc.: North-Holland., 1986. [3690] E.I. Sychev and V.N. Chramenkov. Investigation of a random search algorithm with adaptive structure as for optimization of functions that do not fit the method of statistical experiment. In Applica- tions of random search to the solution of applied problems, Interuniv. Collect. sci. Works, Kemerovo 1981, 23-28, 1981. [3691] W. Syski. A method of stochastic subgradients with complete feedback stepsize rule for convex stochastic approximation problems. J. Optim. Theory Appl., 59(3):487–504, 1988. [3692] Wojciech Syski. Stochastic approximation method with subgradient filtering and on-line stepsize rules for nonsmooth, nonconvex and unconstrained problems. Control Cybernet., 16(1):59–77, 1987. [3693] L.P. Sysoev. Training procedures which combine stochastic approximation and minimization of the empirical risk. Automat. Remote Control, 34(3, part 1):398–411, 1973. [3694] K. Szajowski. Optimal stopping of a sequence of maxima over an unobservable sequence of maxima. Zastosow. Mat. 18, 359-374, 1984. [3695] T. Szantai. Evaluation of a special multivariate gamma distribution function. Math. Program. Study 27, 1-16, 1986. [3696] T. Szantai.´ A computer code for solution of probabilistic-constrained stochastic programming problems. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 229–235. Springer, Berlin, 1988. [3697] T. Szantai.´ Bounds for the reliability of k-out-of-connected-.r; s/-from-.m; n/: F lattice systems. In Stochastic programming methods and technical applications (Neubiberg/Munich, 1996), pages 223–237. Springer, Berlin, 1998. [3698] Tamas´ Szantai.´ On the numerical solution of the stochastic programming model STABIL of Prekopa.´ Alkamaz. Mat. Lapok, 2(1–2):93–101, 1976. [3699] D. Szasz. Ueber ein nichtlineares Optimierungsproblem. Studia Sci. math. Hungar. 93-100 (1975)., 1974. [3700] Krzysztof Szkatula. The growth of multi-constraint random knapsack with various right-hand sides of the constraints. Eur. J. Oper. Res. 73, No.1, 199-204, 1994. [3701] Wlodzimierz Szkutnik. ."; /-confidence set of solutions of a linear stochastic programming problem. Przeglk ad Statyst., 25(3):441–449 (1979), 1978. [3702] Wlodzimierz Szkutnik. On the solution of stochastic linear programming problems as E-models with statistical constraints. Przegl. Stat. 32, 137-150, 1985. [3703] Adam Szuba. Stochastic method of searching for a global minimum. Arch. Automat. Telemech., 25(2):179–188, 1980. [3704] S. Takriti and J. R. Birge. Using integer programming to refine Lagrangian-based unit commitment solutions. IEEE Transactions on Power Systems, 15(1):151–156, 2000.

207 [3705] S. Takriti and J.R. Birge. Lagrangian solution techniques and bounds for loosely-coupled mixed- integer stochastic programs. Technical report, University of Michigan, 1995. [3706] S. Takriti, J.R. Birge, and E. Long. A stochastic model of the unit commitment problem. IEEE Transactions on Power Systems 11(3):1497–1508, 1996. [3707] S. Takriti, B. Krasenbrink, and L. S. Y. Wu. Incorporating fuel constraints and electricity spot prices into the stochastic unit commitment problem. Operations Research, 48(2):268–280, 2000. [3708] S. Takriti, C. Supatgiat, and L. S. Y. Wu. Coordinating fuel inventory and electric power generation under uncertainty. IEEE Transactions on Power Systems, 16(4):603–608, 2001. [3709] Samer Takriti and Shabbir Ahmed. On robust optimization of two-stage systems. Math. Program., 99(1, Ser. A):109–126, 2004. [3710] Samer Takriti and John R. Birge. Lagrangian solution techniques and bounds for loosely coupled mixed-integer stochastic programs. Oper. Res., 48(1):91–98, 2000. [3711] Samer Takriti and John R. Birge. Lagrangian solution techniques and bounds for loosely coupled mixed-integer stochastic programs. Oper. Res., 48(1):91–98, 2000. [3712] Mitsushi Tamaki. A generalized secretary problem with uncertain employment. Surikaisekikenky¯ usho¯ Koky¯ uroku¯ , 864:154–163, 1994. Mathematical structure of optimization theory (Japanese) (Kyoto, 1993). [3713] E. Tamm. Extremum problems depending on a random parameter. In Stochastic optimization, Proc. Int. Conf., Kiev/USSR 1984, Lect. Notes Control Inf. Sci. 81, 585-590, 1986. [3714] Ebu Tamm. The quasiconvexity of the probability function and the quantile function. Eesti. NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 25(2):141–145, 1976. [3715] Ebu Tamm. Cebyˇ sevˇ type inequalities for the solution of E-models of nonlinear stochastic programming. Eesti NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 27(4):448–450, 1978. [3716] Ebu Tamm. On the minimization of the probability function. Izv. Akad. Nauk Ehst. SSR, Fiz., Mat. 28, 17-24, 1979. [3717] Ebu Tamm. Inequalities for the solutions of nonlinear programming problems depending on a random parameter. Math. Operationsforsch. Statist. Ser. Optim., 11(3):487–497, 1980. [3718] Ebu Tamm. On minimization of a function under an equality chance constraint. Math. Operations- forsch. Statist. Ser. Optim., 12(2):253–262, 1981. [3719] Ebu Tamm. Solvability of a problem of nonlinear programming with a random parameter. Eesti NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 30(3):220–225, 294, 1981. [3720] Ebu Tamm. Approximation of a random solution in extremum problems. Kybernetika (Prague), 23(6):483–488, 1987. [3721] Ebu Tamm. Approximation of an unconstrained minimum using biased estimate of the goal function. Eesti Tead. Akad. Toimetised Fuüs.¨ Mat., 41(1):1–6, 74, 1992. [3722] Ebu Tamm. On statistical estimation of a probability function. Eesti Tead. Akad. Toimetised Fuüs.¨ Mat., 41(4):248–252, 1992. [3723] Ehbu Tamm. On the solvability of a problem of nonlinear programming with a random parameter. Izv. Akad. Nauk Ehst. SSR, Fiz., Mat. 30, 220-225, 1981. [3724] K. Tammer. Loesungsbegriffe und Loesungsmoeglichkeiten fuer Optimierungsprobleme mit zu- fallsbehafteter Zielfunktion. In 21. int. wiss. Kolloq.; Ilmenau 1976, Heft 3, 41-44, 1976.

208 [3725] K. Tammer. On the solution of the distribution problem of stochastic programming. In Progress in operations research, Vols. I, II (Proc. Sixth Hungarian Conf., Eger, 1974), pages 907–920. Colloq. Math. Soc. Janos´ Bolyai, Vol. 12, Amsterdam, 1976. North-Holland. [3726] K. Tammer. Behandlung stochastischer Optimierungsprobleme unter dem Gesichtspunkt der Strategie der Vektoroptimierung. Wiss. Z., Tech. Hochsch. Leipz. 4, 295-302, 1980. [3727] Klaus Tammer. Allgemeine Losungsbegriffe¨ fur¨ stochastische Optimierungsprobleme mit festem Restriktionsbereich. Wiss. Z. Humboldt-Univ. Berlin Math.-Natur. Reihe, 26(5):595–602, 1977. [3728] Klaus Tammer. Relations between stochastic and parametric programming for decision problems with a random objective function. Math. Operationsforsch. Statist. Ser. Optim., 9(4):523–535, 1978. [3729] Klaus Tammer. Ueber den Zusammenhang von parametrischer Optimierung und Entschei- dungsproblemen der stochastischen Optimierung. In Anwendungen der linearen parametrischen Optimierung, 76-91, 1979. [3730] Kunio Tanabe. The conjugate gradient method for computing all the extremal stationary probability vectors of a stochastic matrix. Ann. Inst. Statist. Math., 37(1):173–187, 1985. [3731] H. Tanaka, H. Ichihashi, and K. Asai. Decision and information in fuzzy linear programming problems. In Analysis of fuzzy information, Vol. 3: Appl. eng. sci., 265-271, 1987. [3732] Yutaka Tanaka. Optimal scaling for arbitrarily ordered categories. Ann. Inst. Statist. Math., 31(1):115–124, 1979. [3733] Hao Tang and Elise Miller-Hooks. Solving a generalized traveling salesperson problem with stochastic customers. Comput. Oper. Res., 34(7):1963–1987, 2007. [3734] Hao Tang, Hong Sheng Xi, and Bao Qun Yin. On-line optimization algorithm for Markov control processes based on a single sample path. Control Theory Appl., 19(6):865–871, 2002. [3735] Heng Yong Tang. A dual parallel algorithm for stochastic linear programs with simple recourse. Acta Math. Appl. Sinica, 12(3):362–367, 1989. [3736] Heng Yong Tang. A dual contact plane algorithm for problems with probabilistic constraints. Acta Math. Appl. Sinica, 18(1):147–151, 1995. [3737] Hengyong Tang. Penalty function methods for two-period stochastic linear programs with simple recourse. Numer. Math., Nanking 9, No.3, 285-288, 1987. [3738] Li Xin Tang, Zi Hou Yang, and Meng Guang Wang. The lot sizing problem for MRP-II under CIMS. Control Theory Appl., 14(3):376–382, 1997. [3739] Qian-Yu Tang, Pierre L’Ecuyer, and Han-Fu Chen. Central limit theorems for stochastic optimization algorithms using inﬁnitesimal perturbation analysis. Discrete Event Dyn. Syst., 10(1-2):5–32, 2000. [3740] Z. B. Tang. Optimal sequential sampling policy of partitioned random search and its approximation. J. Optim. Theory Appl., 98(2):431–448, 1998. [3741] Z. Bo Tang. Adaptive partitioned random search to global optimization. IEEE Trans. Automat. Control, 39(11):2235–2244, 1994. [3742] Matthew W. Tanner and Eric B. Beier. Tabu search for probabilistically constrained stochastic programs with application to vaccine allocation. Optimization Online, http://www. optimization-online.org, 2007.

209 [3743] Charles S. Tapiero. Optimal control of a stochastic model of advertising. In Optimal control theory and economic analysis, Workshop, Vienna 1981, 287- 300, 1982. [3744] Charles S. Tapiero, Arnold Reisman, and Peter Ritchken. Product failures, manufacturing reliability and quality control: A dynamic framework. INFOR 25, 152-164, 1987. [3745] Charles S. Tapiero and Agnes Sulem. Computational aspects in applied stochastic control. Comput. Econ. 7, No.2, 109-146, 1994. [3746] George S. Tarasenko. Stochastic optimization in the Soviet Union. Monograph Series on Soviet Union. Delphic Associates, Falls Church, VA, 1985. Random search algorithms, With a foreword by Lennart Ljung. [3747] G.S. Tarasenko. Estimate of the convergence rate of an adaptive random search method. Problemy Sluchain. Poiska, 8:162–185, 334, 1980. Voprosy Strukturnoi Adaptatsii. [3748] R. Tarres. Asymptotic evolution of a stochastic control problem when the discount vanishes. As- terisque 75-76, 227-237, 1980. [3749] R. Tavast. Estimation of the admissible set in programming problems with stochastic constraints. Eesti NSV Tead. Akad. Toimetised Fu¨us.-Mat.¨ , 20:478–480, 1971. [3750] S. Tayur. A new algorithm to solve stochastic integer programs with application to plant management. Technical report, Carnegie Mellon University, Pittsburgh, (in preparation). [3751] S.R. Tayur, R.R. Thomas, and N.R. Natraj. An algebraic geometry algorithm for scheduling in the presence of setups and correlated demands. Mathematical Programming, 69(3):369–401, 1995. [3752] J. Teghem. “STRANGE”: an interactive method for multiobjective stochastic linear programming, and “STRANGE-MOMIX”: its extension to integer variables. In Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, volume 6 of Theory Decis. Lib. Ser. D System Theory Knowledge Engrg. Probl. Solving, pages 103–115. Kluwer Acad. Publ., Dordrecht, 1990. [3753] J. Teghem. New developments in multiobjective stochastic linear programming. In Applied stochastic models and data analysis, Vol. I, II (Chania, 1993), pages 938–948. World Sci. Pub- lishing, River Edge, NJ, 1993. [3754] J.jun. Teghem, D. Dufrane, M. Thauvoye, and P. Kunsch. STRANGE: An interactive method for multi-objective linear programming under uncertainty. Eur. J. Oper. Res. 26, 65-82, 1986. [3755] Jr. Teghem, Jacques. Multiobjective and stochastic linear programming. Found. Control Engrg., 8(3-4):225–232 (1984), 1983. Special issue on the 18th meeting of the EURO working group on multicriteria decision aid (Poznan,´ 1983). [3756] Tejada-Guibert, S. A. Johnson, and J. R. Stedinger. The value of hydrologic information in stochastic dynamic programming models of a multireservoir system. Water Resources Research, 31:2571– 2579, 1995. [3757] D. Teneketzis, H. Javid, and B. Sridhar. Operations scheduling by Markov chains with strong and weak interactions. In Electric power problems: the mathematical challange, Proc. Conf., Seattle/Wash. 1980, 426-436, 1980. [3758] L. A. Terry, M. V. F. Pereira, T. A. Araripe Neto, L. E. C. A. Pinto, and P. R. H. Sales. Coordi- nating the energy generation of the Brazilian national hydrothermal electrical generating system. INTERFACES, 16(1):16–38, 1986. [3759] Vitautas Teshis. On the numerical rate and efﬁciency of some global minimization algorithms. Teor. Optim. Reshenij 6, 95-105, 1980.

210 [3760] M.A.L. Thathachar and K.R. Ramakrishnan. On line optimization with a team of learning automata. In Theory and application of digital control, Proc. IFAC Symp., New Delhi 1982, 297-302, 1982. [3761] J. Theni´ e,´ Ch. van Delft, and J.-Ph. Vial. Automatic formulation of stochastic programs via an algebraic modeling language. Comput. Manag. Sci., 4(1):17–40, 2007. [3762] Julien Theni´ e´ and Jean-Philippe Vial. Step decision rules for multistage stochastic programming: a heuristic approach. Optimization Online, http://www.optimization-online.org, 2006. [3763] R. Theodorescu. Minimax solutions of random convex programs. Atti Accad. Naz. Lincei, Rend., Cl. Sci. Fis. Mat. Nat., VIII. Ser. 46, 689-692, 1969. [3764] R. Theodorescu. Random programs. In Math. Aspects Life Sci., Queen’s Papers pure appl. Math. 26, 20-94, 1971. [3765] Radu Theodorescu. Random programs. Math. Operationsforsch. Statist., 3(1):19–47, 1972. [3766] Radu Theodorescu. The minimax principle and random programs. Rend. Circ. Mat. Palermo (2), 28(1):151–160, 1979. [3767] Lionel Thibault. Esperances´ conditionnnelles d’integrandes´ lipschitziens et d’integrandes´ semi- continus inferieurement.´ C.R. Acad. Sci. Paris Ser.´ A-B, 291(9):A551–A554, 1980. [3768] P. Thoft-Christensen. Application of stochastic methods in optimization. Wiss. Z. Hochschule Architektur Bauwesen Weimar 22, 239-244, 1975. [3769] P. Thoft-Christensen. Stochastic modeling and optimization of complex infrastructure systems. In System modeling and optimization, volume 166 of IFIP Int. Fed. Inf. Process., pages 109–122. Kluwer Acad. Publ., Boston, MA, 2005. [3770] G.L. Thompson, W.W. Cooper, and A. Charnes. Characterizations by chance-constrained programming. In Recent Advances math. Program., 113-120, 1963. [3771] Howard E. Thompson, John P. Matthews, and Bob C.L. Li. Insurance exposure and investment risks: An analysis using chance- constrained programming. Operations Res. 22, 991-1007, 1974. [3772] John T. Thorpe and Jr. Harris, Frederick C. A parallel stochastic optimization algorithm for ﬁnding mappings of the rectilinear minimal crossing problem. Ars Combin., 43:135–148, 1996. [3773] G. Thurner. Stochastische Optimierung des Ablaufs von Linienbaustellen. In VI. internat. Kongr. Anwend. Math. Ingenieurwiss., Weimar 1972, 138-142 , 1974. [3774] S¸t. T¸igan and I.M. Stancu-Minasian. The stochastic max-min problem. In Contributions to operations research and mathematical economics, Vol. I, volume 51 of Methods Oper. Res., pages 119–126. Athenaum/Hain/Hanstein,¨ Konigstein/Ts.,¨ 1984. [3775] S¸tefan T¸igan and I.M. Stancu-Minasian. The stochastic max-min problem. Cahiers Centre Etudes´ Rech. Oper.´ , 27(3-4):247–254, 1985. [3776] Stefan Tigan and I.M. Stancu-Minasian. The stochastic bottleneck transportation problem. Math., Rev. Anal. Numer. Theor. Approximation, Anal. Numer. Theor. Approximation 14, 153-158, 1985. [3777] Stephan Tigan and I.M. Stancu-Minasian. Methods for solving stochastic bilinear fractional max- min problems. RAIRO Rech. Oper.´ , 30(1):81–98, 1996. [3778] A.S. Tikhomirov. Markov sequences as optimization algorithms. In Model-oriented data analysis (Petrodvorets, 1992), Contrib. Statist., pages 249–256. Physica, Heidelberg, 1993.

211 [3779] A.S. Tikhomirov. Combinations of global and local search methods as optimization algorithms. Zh. Vychisl. Mat. i Mat. Fiz., 36(9):50–59, 1996. [3780] A.N. Tikhonov, F.P. Vasil’ev, M.M. Potapov, and A.D. Yurij. Regularization of minimization problems on approximately specified sets. Mosc. Univ. Comput. Math. Cybern. 1977, No.1, 2-14 translation from Vestn. Mosk. Univ., Ser. XV 1977, No.1, 4-19 (1977)., 1977. [3781] G. Timmel. Modifikationen eines statistischen Suchverfahrens der Vektoroptimierung. Wiss. Z. Tech. Hochsch. Ilmenau, 28(5):139–148, 1982. [3782] G. A. Timofeeva. Efficient control in multistage stochastic optimization problem. In Proceedings of the 4th International Conference on Mathematical Methods in Operations Research and 6th Workshop on Well-posedness and Stability of Optimization Problems (Sozopol, 1997), volume 12, pages 235–244, 1998. [3783] G. A. Timofeeva. Correction of efficient solutions in a multistep stochastic optimization problem. Izv. Akad. Nauk Teor. Sist. Upr., (1):48–54, 2001. [3784] F. Tin-Loi, L. Qi, Z. Wei, and R.S. Womersley. Stochastic ultimate load analysis: models and solution methods. Numer. Funct. Anal. Optim., 17(9-10):1029–1043, 1996. [3785] C.-J. Ting and P. Schonfeld. Optimization through simulation of waterway transportation investments. Transportation Research Record, no. 1620:11–16, 1998. [3786] K.A. Tinn and E.` H. Tyugu. Nonlinear programming with random constraints. Kibernetika (Kiev), 1:54–62, 1968. [3787] Gerhard Tintner. Stochastic programming and stochastic control. Trab. Estad. Invest. Oper. 26, 487-499, 1975. [3788] Gerhard Tintner and M.V.Rama Sastry. A note on the use of nonparametric statistics in stochastic linear programming. Management Sci., Appl. 19, 205-210, 1972. [3789] Gerhard Tintner and Jati K. Sengupta. Stochastic economics. Stochastic processes, control, and programming. New York-London: Academic Press., 1972. [3790] Cristian-Ioan Tiu and Thaleia Zariphopoulou. On level curves of value functions in optimization models of expected utility. Math. Finance, 10(2):323–338, 2000. INFORMS Applied Probability Conference (Ulm, 1999). [3791] R.N. Tiwari, S. Dharmar, and J.R. Rao. Fuzzy goal programming - an additive model. Fuzzy Sets Syst. 24, 27-34, 1987. [3792] Pavel Tlusty. Deviations from asymptotic normality for optimal solutions of stochastic programming problems. Commentat. Math. Univ. Carol. 33, No.1, 188, 1992. [3793] T. Tobias. Kuhn-Tucker conditions for the two-phase stochastic programming problem with integral constraints. Eesti NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 27(1):3–8, 1978. [3794] T. Tobias. Lagrange multipliers in linear multistage stochastic programming problems. Eesti NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 28(2):97–100, 1979. [3795] T. Tobias. Approximation method for the solution of programming problems with operator constraints. Eesti NSV Tead. Akad. Toimetised Fuüs.-Mat.¨ , 29(1):101–104, 111, 1980. [3796] M. J. Todd. Erratum: “Probabilistic models for linear programming” [Math. Oper. Res. 16 (1991), no. 4, 671–693; MR 93a:90042]. Math. Oper. Res., 23(3):767–768, 1998. [3797] Michael J. Todd. Probabilistic models for linear programming. Math. Oper. Res., 16(4):671–693, 1991.

212 [3798] Yesim Tokat, Svetlozar T. Rachev, and Eduardo Schwartz. The stable non-Gaussian asset allocation: A comparison with the classical Gaussian approach. Stochastic Programming E-Print Series, http://www.speps.org, 2000. [3799] Berkin Toktas, Joyce W. Yen, and Zelda B. Zabinsky. A stochastic programming approach to resource-constrained assignment problems. Stochastic Programming E-Print Series, http:// www.speps.org, 2004. [3800] B. Tolwinski. The approximate method for solving dynamic optimisation problems. In 18. internat. wiss. Kolloqu., Ilmenau 1, 65-67, 1973. [3801] A. Tomasgard, J.A. Audestad, S. Dye, L. Stougie, M.H. van der Vlerk, and S.W. Wallace. Mod- elling aspects of distributed processing in telecommunication networks. Annals of Operations Research, 82:161–184, 1998. [3802] A. Tomasgard, S. Dye, S.W. Wallace, J.A. Audestad, L. Stougie, and M.H. van der Vlerk. Stochas- tic optimization models for distributed communication networks. Working paper, Department of Industrial Economics and Technology Management, Norwegian University of Science and Tech- nology, 7034 Trondheim, Norway, 1997. [3803] Nikolas Topaloglou, Hercules Vladimirou, and Stavros A. Zenios. CvaR models with selective hedging for international asset allocation. Journal of Banking and Finance, 26(7):1535–1561, 2002. [3804] Huseyin Topaloglu and Warren B. Powell. An algorithm for approximating piecewise linear concave functions from sample gradients. Oper. Res. Lett., 31(1):66–76, 2003. [3805] V.V. Topka. A probabilistic model for planning research and development under linear constraints. Avtomat. i Telemekh., 4:232–237, 1997. [3806] A.F. Torondzhadze. On an information-statistical method for solving multi-extremal problems. Tr., Vychisl. Tsentr Im. N. I. Muskhelishvili 21, No.2, 56-66, 1981. [3807] Vassili V. Toropov. Multipoint approximation method for structural optimization problems with noisy function values. In Stochastic programming (Neubiberg/Munchen,¨ 1993), volume 423 of Lecture Notes in Econom. and Math. Systems, pages 109–122. Springer, Berlin, 1995. [3808] Norio Baba Toshio Shoman and Yoshikazu Sawaragi. A modified convergence theorem for a random optimization method. Inform. Sciences 13, 159-166, 1977. [3809] Tasuku Toyonaga, Takeshi Itoh, and Hiroaki Ishii. A crop planning problem with fuzzy random profit coefficients. Fuzzy Optim. Decis. Mak., 4(1):51–69, 2005. [3810] Jui-Fen C. Trappey, C.Richard Liu, and Tien-Chien Chang. Fuzzy nonlinear programming: Theory and application in manufacturing. Int. J. Prod. Res. 26, No.5, 975-985, 1988. [3811] Grigori L. Tretiakov. Star-shaped approximation approach for stochastic programming problems with probability function. Optimization, 47(3-4):303–317, 2000. Numerical methods for stochastic optimization and real-time control of robots (Neubiberg/Munich, 1998). [3812] Grigoriy Tretiakov. Stochastic quasi-gradient algorithms for maximization of the probability function. A new formula for the gradient of the probability function. In Stochastic optimization techniques (Neubiberg/Munich, 2000), volume 513 of Lecture Notes in Econom. and Math. Systems, pages 117–139. Springer, Berlin, 2002. [3813] V.E. Tret’yakov. Program synthesis in a stochastic differential game. Sov. Math., Dokl. 27, 610-614 translation from Dokl. Akad. Nauk SSSR 270, 297-300 (1983)., 1983. [3814] V.E. Tret’yakov. Synthesis of optimal guaranteeing control. Probl. Control Inf. Theory 17, No.4, 207-221, 1988.

213 [3815] M.D. Troutt and T.B. Paine. A monotone variational method for optimal probability distributions. OR Spektrum, 12(4):201–206, 1990. [3816] Alain Trouve.´ Noyaux partiellement synchrones et parallelisation´ du recuit simule.´ C.R. Acad. Sci. Paris Ser.´ I Math., 312(1):155–158, 1991. [3817] A. Truffert. Conditional expectation of integrands and random sets. Ann. Oper. Res., 30(1-4):117– 156, 1991. Stochastic programming, Part I (Ann Arbor, MI, 1989). [3818] G. Trzpiot. Multivalued limit laws applied to stochastic optimization. Random Oper. Stochastic Equations, 3(4):309–314, 1995. [3819] P. Tsamasphyrou, A. Renaud, and P. Carpentier. Transmission network planning under uncertainty with benders decomposition. Lecture Notes in Economics and Mathematical Systems, 481:457– 472, 2000. [3820] H.S.J. Tsao, S.C. Fang, and D.N. Lee. On the optimal entropy analysis. Eur. J. Oper. Res. 59, No.2, 324-329, 1992. [3821] Chung-Li Tseng and Graydon Barz. Short-term generation asset valuation: a real options approach. Oper. Res., 50(2):297–310, 2002. [3822] A.M. Tsirlin. Conditions for optimality of the solution of averaged problems of mathematical programming. Dokl. Akad. Nauk, 323(1):43–47, 1992. [3823] G. Sh. Tsitsiashvili. Parallelization of stochastic programming algorithms. Issled. Operatsii i ASU, 35:3–11, 1991. [3824] G.Sh. Tsitsiashvili. Decomposition methods in problems of stability and efﬁciency of complex systems. (Dekompozitsionnye metody v zadachakh ustojchivosti i ehffektivnosti slozhnykh sistem). Vychislitel’nyj Tsentr Dal’nevostochnogo Otdeleniya AN SSSR, Vladivostok, 1989. [3825] John N. Tsitsiklis. A survey of large time asymptotics of simulated annealing algorithms. In Stochastic differential systems, stochastic control theory and applications (Minneapolis, Minn., 1986), volume 10 of IMA Vol. Math. Appl., pages 583–599. Springer, New York, 1988. [3826] E.` V. Tsoi. Solvability of certain classes of multistage stochastic programming problems with arbitrary information structure. Cybernetics, 16(4):619–620 (1981), 1980. [3827] Eh.V. Tsoj. On a class of inﬁnite-stage problems of stochastic programming. Kibernetika 1980, No.5, 144-145, 1980. [3828] Ioannis G. Tsoulos and Isaac E. Lagaris. Genetically controlled random search: a global optimization method for continuous multidimensional functions. Comput. Phys. Comm., 174(2):152–159, 2006. [3829] V.I. Tsurkov. A two-stage stochastic programming problem of the block type. U.S.S.R. Comput. Math. Math. Phys. 18, No.2, 66-75, 1978. [3830] Ya. Z. Tsypkin. Adaptive decision-making methods under uncertainty conditions. Automat. Remote Control, 37(4, part 1):544–556, 1976. [3831] Ya. Z. Tsypkin, A.I. Kaplinskiy, and A.S. Krasnenker. Methods of local improvement in stochastic optimization problems. Engrg. Cybernetics, 11(6):889–897, 1973. [3832] Ya. Z. Tsypkin and A.S. Poznyak. Optimal and robust optimization algorithms in the presence of correlated noise. Dokl. Akad. Nauk SSSR, 258(6):1330–1333, 1981. [3833] Ya. Z. Tsypkin and A.S. Poznyak. Optimal search algorithms for stochastic optimization. Dokl. Akad. Nauk SSSR, 260(3):550–553, 1981.

214 [3834] Ya. Z. Tsypkin and A.S. Poznyak. Recursive algorithms for optimization under conditions of uncertainty. In Engineering cybernetics, Vol. 16, Itogi Nauki i Tekhniki, pages 3–70. Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1983. [3835] Ya.Z. Tsypkin. Optimality in problems and optimization algorithms under indeterminacy. Autom. Remote Control 47, 67-72 translation from Avtom. Telemekh. 1986, No.1, 75-80 (1986)., 1986. [3836] Ya.Z. Tsypkin, A.S. Poznyak, and A.M. Pesin. Search algorithms for criterial optimization under conditions of uncertainty. Sov. Phys., Dokl. 28, 367-369 translation from Dokl. Akad. Nauk SSSR 270, 565-568 (1983)., 1983. [3837] A.D. Tuniev. A certain approach to the solution of stochastic programming problems. In Theory of optimal solutions (Proc. Sem., Kiev, 1968), No. 3 (Russian), pages 42–49, Kiev, 1969. Akad. Nauk Ukrain. SSR. [3838] A. Turgeon. Optimal operation of multireservoir power systems with stochastic inﬂows. Water Resources Research, 16:275–283, 1980. [3839] Alexandre Turull. Clifford theory with Schur indices. J. Algebra 170, No.2, 661-677, 1994. [3840] E. Ubi. Finding an optimal random solution of M-and P-models in stochastic programming. Izv. Akad. Nauk Ehst. SSR, Fiz. Mat. 26, No.1, 64-71, 1977. [3841] E. Uebi. Statistical investigation of stochastic programming problems and a method for their solution. Izv. Akad. Nauk Ehst. SSR, Fiz. Mat. 26, 369-375, 1977. [3842] Fevzi Uenlue. Unconstrained probabilistic goal programming by the least square adjustment to ﬁnite convolution. In Applications of mathematics in system theory, Proc. int. Symp., Brasov/Romania 1978, Vol. II, 189-195, 1979. [3843] Takayuki Ueno and Seiichi Iwamoto. On past accumulation values and future threshold values in stochastic optimization. Surikaisekikenky¯ usho¯ Koky¯ uroku¯ , (1207):79–100, 2001. Perspective and problems for dynamic programming with uncertainty (Japanese) (Kyoto, 2001). [3844] B. Uhrin. Brunn-Minkowski-Lusternik inequality, its sharpenings, extensions and some applications. Kozl.¨ MTA Szamit´ astech.´ Automat. Kutato´ Int. Budapest, 39:151–194, 1988. [3845] B. Uhrin. Two types of random polyhedral sets. Kozl.¨ MTA Szamit´ astech.´ Automat. Kutato´ Int. Budapest, 39:131–149, 1988. [3846] S. Ul’m. Zu Methoden der hierarchischen Optimierung. Izv. Akad. Nauk Eston. SSR, Fiz. Mat. 21, 208-211, 1972. [3847] Universidad de la Habana Departamento de Matematica´ Aplicada. Workshop on Stochastic Op- timization: the State of the Art, Havana, 1993. Papers from the workshop held in Havana, April 1992, Investigacion´ Oper. 14 (1993), no. 2-3. [3848] S. Urasiev. Adaptive stochastic quasigradient procedures. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 373–384. Springer, Berlin, 1988. [3849] Andrzej Urbaniak. A method of a choice of an expansion strategy of the water supply system with random parameters. Found. Control Eng. 10, 143-159, 1985. [3850] S.P. Urjas’ev. Adaptive control of parameters in gradient algorithms for stochastic optimization. In Stochastic optimization (Kiev, 1984), volume 81 of Lecture Notes in Control and Inform. Sci., pages 591–601. Springer, Berlin, 1986. [3851] Bruno Urli and Raymond Nadeau. Multiobjective stochastic linear programming with incomplete information: a general methodology. In Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, volume 6 of Theory Decis. Lib. Ser. D System Theory Knowledge Engrg. Probl. Solving, pages 131–161. Kluwer Acad. Publ., Dordrecht, 1990.

215 [3852] Bruno Urli and Raymond Nadeau. Stochastic MOLP with incomplete information: An interactive approach with recourse. J. Oper. Res. Soc. 41, No.12, 1143-1152, 1990. [3853] Veniamin Al. Urseanu. Models of stochastic optimization and the price systems. Econom. Comput. econom. Cybernetics Studies Res. 1973, Nr. 4, 63-76, 1973. [3854] S. Uryasev. Analytic perturbation analysis of discrete event dynamic systems. In Proc. Fourth International Conference on Computer Integrated Manufacturing & Automated Technology, pages 397–402, Troy, NY., 1994. IEEE Computer Society Press. [3855] S. Uryasev. Derivatives of probability functions and integrals over sets given by inequalities. J. Computational and Applied Mathematics, 56:197–223, 1994. [3856] S. Uryasev. New formulas for the derivatives of integrals and application to a shut down problem. In Proc. International Conference on Mathematics and Computations, Reactor Physics, and Environmental Analyses, pages 689–698, Portland, Oregon, 1995. American Nuclear Society. [3857] S. Uryasev and Vallerga H. Optimization of test strategies - a general approach. Reliability Engi- neering & Systems Safety, 41:155–165, 1993. [3858] S.P. Uryas’ev. Step control for direct stochastic-programming methods. Cybernetics, 16(6):886– 890 (1981), 1980. [3859] S.P. Uryas’ev. On step length adjustment in limiting extremum problems. Cybernetics, 17(1):117– 121, 1981. [3860] S.P. Uryas’ev. Arrow-Hurwitz algorithms with adaptively controlled increment multipliers. Issled. Oper. ASU 24, 3-11, 1984. [3861] S.P. Uryas’ev. Differentiability of the integral over a set deﬁned by inclusion. Cybernetics 24, No.5, 638-642 translation from Kibernetika 1988, No.5, 83-86 (1988)., 1988. [3862] S.P. Uryas’ev. Adaptive algorithms of stochastic optimization and game theory. (Adaptivnye algoritmy stokhasticheskoj optimizatsii i teorii igr). Ed. by Yu. M. Ermol’ev. Nauka, Moskwa, 1990. [3863] S.P. Uryas’ev. Adaptivnye algoritmy stokhasticheskoi optimizatsii i teorii igr. “Nauka”, Moscow, 1990. Edited and with a preface by Yu. M. Ermol’ ev, With an English summary. [3864] S.P. Uryas’ev. A stochastic quasigradient algorithm with variable metric. Ann. Oper. Res., 39(1- 4):251–267 (1993), 1992. [3865] Stanislav Uryasev. Derivatives of probability functions and some applications. Ann. Oper. Res., 56:287–311, 1995. Stochastic programming (Udine, 1992). [3866] Stanislav Uryasev and Panos M. Pardalos, editors. Stochastic optimization: algorithms and applications. Kluwer Academic Publishers, Dordrecht, 2001. Papers from the conference held at the University of Florida, Gainesville, FL, February 20–22, 2000. [3867] Stanislav Uryasev and R. Tyrrell Rockafellar. Conditional value-at-risk: optimization approach. In Stochastic optimization: algorithms and applications (Gainesville, FL, 2000), volume 54 of Appl. Optim., pages 411–435. Kluwer Acad. Publ., Dordrecht, 2001. [3868] Stanislav P. Uryasev, editor. Probabilistic constrained optimization. Kluwer Academic Publishers, Dordrecht, 2000. Methodology and applications. [3869] I.A. Ushakov and E.I. Gordienko. Ueber ein statistisches Verfahren zur Loesung gewisser Opti- mierungsprobleme. Elektron. Informationsverarbeitung Kybernetik 14, 585-592, 1978. [3870] N. Uteuliev. Optimality conditions and duality relations for a class of multistage problems of stochastic nonlinear programming. Issled. Operatsii i ASU, 32:39–42, 117, 1988.

216 [3871] I. Vaduva and G. Ciobanu. The ”duration - resource” relation in PERT type problems with resources. Econom. Comput. econom. Cybernetics Studies Res. 1973, Nr. 1, 61-78, 1973. [3872] A.G. Vainstein, V.P. Suckov, and A.M. Cirlin. Ueber Abschaetzungen der Loesung des Problems der nichtlinearen Programmierung im Mittel. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1976, Nr. 1, 29-33, 1976. [3873] S. Vajda. Stochastic programming. In J. Abadie, editor, Integer and nonlinear programming, pages 321–336. North-Holland, Amsterdam, 1970. [3874] S. Vajda. Probabilistic programming. Academic Press, New York, 1972. Probability and Mathe- matical Statistics. [3875] S. Vajda. Linear programming. Algorithms and applications. Science Paperbacks, 167. London, New York: Chapman and Hall., 1981. [3876] Stefan Vajda. Deterministic equivalents of probabilistic constraints. In Proceedings of the Second International Seminar on Operational Research in the Basque Provinces (San Sebastian, 1987), pages 253–260, Bilbao, 1988. Univ. País Vasco-Euskal Herriko Unib. [3877] A. T. Vakhitov, O. N. Granichin, and S. S. Sysoev. The accuracy of the estimation of a randomized stochastic optimization algorithm. Avtomat. i Telemekh., (4):86–96, 2006. [3878] P. Valente, G. Mitra, and C. A. Poojari. A stochastic programming integrated environment. In Ap- plications of stochastic programming, volume 5 of MPS/SIAM Ser. Optim., pages 115–136. SIAM, Philadelphia, PA, 2005. [3879] P. Valente, Gautam Mitra, M. Sadki, and R. Fourer. Extending algebraic modelling languages for stochastic programming. Stochastic Programming E-Print Series, http://www.speps.org, 2005. [3880] Bernard Van Cutsem. Problems of convergence in stochastic linear programming. In Techniques of optimization (Fourth IFIP Colloq., Los Angeles, Calif., 1971), pages 445–454, New York, 1972. Academic Press. [3881] Ch. van Delft and J.-Ph. Vial. A practical implementation of stochastic programming: an application to the evaluation of option contracts in supply chains. Automatica J. IFAC, 40(5):743–756 (2005), 2004. [3882] Maarten H. van der Vlerk. Stochastic programming with integer recourse. PhD thesis, University of Groningen, The Netherlands, 1995. [3883] Maarten H. van der Vlerk. Stochastic programming bibliography. World Wide Web, http: //mally.eco.rug.nl/spbib.html, 1996-2007. [3884] Maarten H. van der Vlerk. Convex approximations for stochastic programs with simple integer recourse. In Ten years LNMB, volume 122 of CWI Tract, pages 357–365. Math. Centrum Centrum Wisk. Inform., Amsterdam, 1997. [3885] Maarten H. van der Vlerk. Simplification of recourse models by modification of recourse data. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [3886] Maarten H. van der Vlerk. Convex approximations for complete integer recourse models. Math. Program., 99(2, Ser. A):297–310, 2004. [3887] Maarten H. van der Vlerk. Simplification of recourse models by modification of recourse data. In Dynamic stochastic optimization (Laxenburg, 2002), volume 532 of Lecture Notes in Econom. and Math. Systems, pages 321–336. Springer, Berlin, 2004.

217 [3888] Maarten H. van der Vlerk. Convex approximations for a class of mixed-integer recourse models. Stochastic Programming E-Print Series, http://www.speps.org, 2005. [3889] Maarten H. van der Vlerk. Modification of Recourse Data for Mixed-Integer Recourse Models. In S. Albers, R.H. Mohring,¨ G.Ch. Pflug, and R. Schultz, editors, Dagstuhl Seminar 05031: Algo- rithms for Optimization with Incomplete Information, http://www.dagstuhl.de/05031, 2005. [3890] Maarten H. van der Vlerk, Willem K. Klein Haneveld, and Matthijs H. Streutker. Integrated chance constraints in an alm model for pension funds. Stochastic Programming E-Print Series, http: //www.speps.org, 2003. [3891] M.H. van der Vlerk. Stochastic integer programming bibliography. World Wide Web, http: //mally.eco.rug.nl/spbib.html, 1996-2007. [3892] M.H. van der Vlerk. Stochastic programming with simple integer recourse. In C.A. Floudas and P.M. Pardalos, editors, Encyclopedia of Optimization, volume V, pages 343–346. Kluwer Academic Publishers, 2001. [3893] M.H. van der Vlerk. On multiple simple recourse models. Mathematical Methods of Operations Research, 62(2):225–242, 2005. [3894] J. van der Wal. Stochastic dynamic programming. Successive approximations and nearly optimal strategies for Markov decision processes and Markov games. Mathematical Centre Tracts, 139. Amsterdam: Mathematisch Centrum., 1981. [3895] Paul van Moeseke. Stochastic portfolio programming: the game solution. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 497–505, London, 1980. Academic Press. [3896] Paul van Moeseke. Efficient portfolios: risk shares and monetary policy. In Econometrics of planning and efficiency, volume 11 of Adv. Stud. Theoret. Appl. Econometrics, pages 109–122. Kluwer Acad. Publ., Dordrecht, 1988. [3897] R. Van Slyke and R.J-B. Wets. L-shaped linear programs with applications to control and stochastic programming. SIAM Journal on Applied Mathematics, 17:638–663, 1969. [3898] A. Vande Wouwer, C. Renotte, and M. Remy. On the use of simultaneous perturbation stochastic approximation for neural network training. In Proceedings of the American Control Conference, pages 388–392, 1999. [3899] Pravin Varaiya and Roger J.-B. Wets. Stochastic dynamic optimization approaches and computation. In Mathematical programming (Tokyo, 1988), volume 6 of Math. Appl. (Japanese Ser.), pages 309–331. KTK Scientific, Tokyo, 1989. [3900] Anna Vasarhelyi. Collapse load analysis and optimal design by stochastic programming with uncertainties of loads. In Stochastic optimization. Numerical methods and technical applications, Proc. GAMM/IFIP-Workshop, Neubiberg/Ger. 1990, Lect. Notes Econ. Math. Syst. 379, 173-182, 1992. [3901] S.A. Vasil’kovskij. The solution of stochastic standardization problems. Comput. Math. Math. Phys. 32, No.2, 275-278 translation from Zh. Vychisl. Mat. Mat. Fiz. 32, No.2, 331-335 (1992)., 1992. [3902] A.A. Vasin and N.N. Evtikhiev. Some decision-making problems associated with random walks. Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., 1:19–23, 48, 1997. [3903] Christiana Vassiadou-Zeniou and Stavros A. Zenios. Robust optimization models for managing callable bond portfolios. European Journal of Operations Research, 91:264–273, 1996.

218 [3904] I.A. Vatel’ and V.I. Tsurkov. A two-level system with stochastic parameter constraints. Automat. Remote Control, 41(2, part 2):232–237, 1980. [3905] A.A. Vatolin. Correction of inconsistent linear inequality system with regard to restrictions on parameter variation. In 19. Jahrestagung “Mathematische Optimierung” (Sellin, 1987), volume 90 of Seminarberichte, pages 132–135. Humboldt Univ. Berlin, 1987. [3906] Felisa J. Vazquez-Abad.´ Sensitivity analysis for stochastic DEDS: an overview. In Second Sympo- sium on Probability Theory and Stochastic Processes. First Mexican-Chilean Meeting on Stochas- tic Analysis (Spanish) (Guanajuato, 1992), volume 7 of Aportaciones Mat. Notas Investigacion´ , pages 163–182. Soc. Mat. Mexicana, Mexico´ City, 1992. [3907] A. S. Velichko. A dual truncation algorithm for a two-stage stochastic programming problem. Izv. Vyssh. Uchebn. Zaved. Mat., (4):78–81, 2006. [3908] G.I. Venkov. The identiﬁcation of stochastic systems as a minimax problem. God. Vissh. Uchebn. Zaved., Prilozhna Mat. 1 No.2, 121-128 (1978)., 1977. [3909] P.I. Vercenko.ˇ Limit extremal problems with complex tests. In Systems analysis by operations research and reliability theory methods (Russian), pages 67–78, Kiev, 1975. Inst. Kibernet. Akad. Nauk Ukrain. SSR. [3910] P.I. Verchenko. Solution of limit problems of stochastic programming with general constraints. In Methods of investigation of extremal problems, pages 96–103, 123, Kiev, 1981. Akad. Nauk Ukrain. SSR Inst. Kibernet. [3911] J.L. Verdegay. Fuzzy mathematical programming. In Fuzzy information and decision processes, 231-237, 1982. [3912] Bram Verweij, Shabbir Ahmed, Anton Kleywegt, George Nemhauser, and Alexander Shapiro. The sample average approximation method applied to stochastic routing problems: A computational study. Optimization Online, http://www.optimization-online.org, 2001. [3913] R.P.van der Vet. On the Bellman principle for decision problems with random decision policies. J. Engin. Math. 10, 107-114, 1976. [3914] Rene´ Victor Valqui Vidal. Stochastic version of the economic lot size model. Investigacion´ Oper., 15(1):3–12, 1994. [3915] Stefan Vigerske and Ivo Nowak. Adaptive discretization of convex multistage stochastic programs. Math. Methods Oper. Res., 65(2):361–383, 2007. [3916] J.P. Vila. Exact experimental designs via stochastic optimization for nonlinear regression models. In Computational statistics, Proc. 9th Symp. COMPSTAT, Dubrovnik/Yugosl. 1990, 291-296, 1990. [3917] M.L. Vil’k and S.V. Shil’man. Convergence and optimality of quasi-Newtonian algorithms of stochastic optimization. Dinamika Sistem, 151:3–21, 1985. [3918] M.L. Vil’k and S.V. Shil’man. Convergence and optimality of realizable algorithms for adaptation (informational approach). Problemy Peredachi Informatsii, 21(3):80–88, 1985. [3919] Eh.J. Vilkas and E.Z. Majminas. Decisions: theory, information, simulation. (Resheniya: teoriya, informatsiya, modelirovanie). Moskva: ”Radio i Svyaz”., 1981. [3920] I.M. Vishenchuk, V.V. Trotsenko, and B.I. Shvetskij. Analysis of transiens processes in computing converters for integral signal parameters. Autom. Control Comput. Sci. 12, No.3, 36-43, 1978. [3921] B. V. Vishnyakov and A. I. Kibzun. Deterministic equivalents for stochastic programming problems with probabilistic criteria. Avtomat. i Telemekh., (6):126–143, 2006.

219 [3922] Bela´ Vizvari.´ The integer programming background of a stochastic integer programming algorithm of Dentcheva-Prekopa-Ruszczy´ nski.´ Optim. Methods Softw., 17(3):543–559, 2002. Stochastic programming. [3923] H. Vladimirou, S.A. Zenios, and R.J.-B. Wets, editors. Models for planning under uncertainty. Baltzer Science Publishers BV, Amsterdam, 1995. Ann. Oper. Res. 59 (1995). [3924] Hercules Vladimirou. Computational assessment of distributed decomposition methods for stochastic linear programs. European Journal of Operational Research, 108:653–670, 1998. [3925] Hercules Vladimirou, Istvan Maros, and Gautam Mitra, editors. Applied Mathematical Program- ming and Modeling IV. Annals of Operations Research, Vol. 99. Kluwer Academic Publishers, 2000. [3926] Hercules Vladimirou and Stavros A. Zenios. Parallel algorithms for large-scale stochastic programming. In P. M. Pardalos A. Migdalas and S. Storoy, editors, Parallel Computing in Optimization, pages 413–461. Kluwer, Dordrecht, 1997. [3927] Hercules Vladimirou and Stavros A. Zenios. Stochastic linear programs with restricted recourse. European Journal of Operations Research, 101:177–192, 1997. [3928] Hercules Vladimirou and Stavros A. Zenios. Stochastic programming and robust optimization. In T. Gal and H. Greenberg, editors, Advances in Sensitivity Analysis and Parametric Programming, chapter 12. Kluwer Academic Publishers, 1997. [3929] Hercules Vladimirou and Stavros A. Zenios. Scalable parallel computations for large-scale stochastic programming. Annals of Operations Research, 90:87–129, 1999. [3930] Hercules Vladimirou and Stavros A. Zenios. Stochastic programming: Parallel factorization of structured matrices. In Encyclopedia of Optimization, Vol. V., pages 338–343. Kluwer Academic Publishers, 2001. [3931] Silvia Vogel. Necessary optimality conditions for two-stage stochastic programming problems. Optimization, 16(4):607–616, 1985. [3932] Silvia Vogel. Stability results for stochastic programming problems. Optimization, 19(2):269–288, 1988. [3933] Silvia Vogel. On stability in multiobjective programming—a stochastic approach. Math. Program- ming, 56(1, Ser. A):91–119, 1992. [3934] Silvia Vogel. Stochastic stability concepts. In Operations research proceedings 1990, Pap. 19th Annu. Meet. DGOR, Vienna/Austria 1990, 57-64, 1992. [3935] Silvia Vogel. A stochastic approach to stability in stochastic programming. J. Comput. Appl. Math., 56(1-2):65–96, 1994. Stochastic programming: stability, numerical methods and applications (Gosen, 1992). [3936] Silvia Vogel. Random approximations in multiobjective programming—with an application to portfolio optimization with shortfall constraints. Control Cybernet., 28(4):703–724, 1999. Portfolio optimization (Laxenburg, 1998). [3937] Silvia Vogel. Stochastic programming and statistical estimates. In Operations Research Proceed- ings 2003, pages 443–450, Berlin, 2004. Springer. [3938] Silvia Vogel. Qualitative stability of stochastic programs with applications in asymptotic statistics. Statist. Decisions, 23(3):219–248, 2005. [3939] Yu. M. Volin and G.M. Ostrovskii. Optimization of technological processes under partial uncertainty about the initial information. Avtomat. i Telemekh., 12:85–98, 1995.

220 [3940] V.A. Volkonskii and S.A. Ivankov. Saetze ueber die Konvergenz iterativer Prozeduren. In Mat. Metody Resen. ekonom. Zadac 3, 37-51, 1972. [3941] Y. V. Volkov and S. K. Zavriev. A general stochastic outer approximations method. SIAM J. Control Optim., 35(4):1387–1421, 1997. [3942] V.L. Volkovic and E.P. Lavrinenko. Das Problem der Kompromissregelung in hierarchischen Sys- temen mit zwei Ebenen unter Beruecksichtigung zufaelliger Stoerungen. Avtomat. vycislit. Tehn., Riga 1973, Nr. 2, 48-55, 1973. [3943] Konstantin Volosov, Gautam Mitra, Fabio Spagnolo, and Cormac Lucas. Treasury management model with foreign exchange exposure. Stochastic Programming E-Print Series, http://www. speps.org, 2004. [3944] E.I. Volynskii, L.I. Poteskina, and G.V. Filatov. Die Verwendung einiger Glaettungs-Operatoren in Extremum-Such-Problemen. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1975, Nr. 2, 90-95, 1975. [3945] H. Voogd. Stochastic multicriteria evaluation by means of geometric scaling. Delft Prog. Rep. 5, 112-125, 1980. [3946] A.N. Voronin. A stochastic problem of multicriterial optimization. Soviet Automat. Control, 17(4):67–69 (1985), 1984. [3947] M.A. Vorontsov, G.W. Carhart, M. Cohen, and G. Cauwenberghs. Adaptive optics based on analog parallel stochastic optimization: Analysis and experimental demonstration. Journal of the Optical Society of America A, 17:1440–1453, 2000. [3948] S.V. Vorozheeva, O.I. Chernykh, and G.D. Chernyshova. Construction of probabilistic algorithms for optimization by means of a modiﬁed Lagrange function for computer-aided design systems problems. In Optimization and modeling in automated systems (Russian), pages 87–90. Voronezh. Politekhn. Inst., Voronezh, 1988. [3949] Michael D. Vose and Jonathan E. Rowe. Random heuristic search: applications to GAs and functions of unitation. Comput. Methods Appl. Mech. Engrg., 186(2-4):195–220, 2000. [3950] Michael D. Vose and Jonathan E. Rowe. Random heuristic search: applications to GAs and functions of unitation. Comput. Methods Appl. Mech. Engrg., 186(2-4):195–220, 2000. [3951] E.N. Voyevudskiy. Stochastic optimisation of queueing system control. In Optimization, Vol. 1, 2 (Singapore, 1992), pages 653–656. World Sci. Publishing, River Edge, NJ, 1992. [3952] Miroslav Voznyakovski and Danuta Zakzhevska. Optimal strategy for testing the fulﬁllment of constraints in iterative algorithms for searching for the extremum of a function. Zeszyty Nauk. Politech. Lodz.´ Mat., 17:87–94, 1984. [3953] M. N. Vyalyi. Local optimization algorithms and the geometry of polyhedra. In Combinatorial models and methods (Russian), pages 15–26. Ross. Akad. Nauk Vychisl. Tsentr, Moscow, 1995. [3954] M. N. Vyalyi. On estimates for the values of a functional in polyhedra of the subgraph of least weight problem. In Combinatorial models and methods (Russian), pages 27–43. Ross. Akad. Nauk Vychisl. Tsentr, Moscow, 1995. [3955] F.de Vylder and M. Goovaerts. Maximization of the variance of a stop-loss reinsured risk. Insur. Math. Econ. 2, 75-80, 1983. [3956] Jan Wachowiak. On a problem of abstract stochastic optimization with nondifferentiable cost function. Funct. Approximatio Comment. Math., 5:106–112, 1977.

221 [3957] Janet M. Wagner and Oded Berman. Models for planning capacity expansion of convenience stores under uncertain demand and the value of information. Ann. Oper. Res., 59:19–44, 1995. Models for planning under uncertainty. [3958] Janet M. Wagner, Uri Shamir, and David H. Marks. Containing groundwater contamination: Plan- ning models using stochastic programming with recourse. Eur. J. Oper. Res. 77, No.1, 1-26, 1994. [3959] Kazumasa Wakimoto. Algorithms for generating a random vector with restricted integer components and their extension to matrix. In Essays in probability and statistics, pages 179–188. Shinko Tsusho, Tokyo, 1976. [3960] Kazuyoshi Wakuta. A method of successive approximations in continuous time Markovian decision processes. Res. Rep. Nagaoka Techn. College 12, 67-71, 1976. [3961] H. Walk. Zur Konvergenzgeschwindigkeit eines rekursiven Penalisationsverfahrens der stochastischen Optimierung. Osterreich.¨ Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, 198(8-10):381–399, 1989. [3962] D. Walkup and R.J-B. Wets. Stochastic programs with recourse. SIAM Journal on Applied Mathe- matics, 15:1299–1314, 1967. [3963] D.W. Walkup and R.J.-B. Wets. Some practical regularity conditions for nonlinear programms. SIAM J. Control 7, 430-436, 1969. [3964] D.W. Walkup and R.J.B. Wets. Stochastic programs with recourse: special forms. In Proceedings of the Princeton Symposium on Mathematical Programming (Princeton Univ., 1967), pages 139–161, Princeton, N.J., 1970. Princeton Univ. Press. [3965] J.van der Wall and J. Wessels. Markov decision processes. Stat. Neerl. 39, 219-233, 1985. [3966] S. W. Wallace, editor. Modelling: in memory of Asa˚ Hallefjord. Baltzer Science Publishers BV, Bussum, 1998. Ann. Oper. Res. 82 (1998). [3967] Stein W. Wallace. Solving stochastic programs with network recourse. Networks, 16(3):295–317, 1986. [3968] Stein W. Wallace. A piecewise linear upper bound on the network recourse function. Math. Pro- gram. 38, 133-146, 1987. [3969] Stein W. Wallace. Investing in arcs in a network to maximize the expected max ﬂow. Networks 17, No.1, 87-103, 1987. [3970] Stein W. Wallace. Bounds on the expected maximal value of a class of stochastic network problems. INFOR 26, No.3, 153-162, 1988. [3971] Stein W. Wallace and Thorkell Helgason. Structural properties of the progressive hedging algorithm. Ann. Oper. Res., 31(1-4):445–455, 1991. Stochastic programming, Part II (Ann Arbor, MI, 1989). [3972] Stein W. Wallace and Roger J.-B. Wets. Preprocessing in stochastic programming: the case of linear programs. ORSA J. Comput., 4(1):45–59, 1992. [3973] Stein W. Wallace and Roger J.-B. Wets. Preprocessing in stochastic programming: the case of capacitated networks. ORSA J. Comput., 7(1):44–62, 1995. [3974] Stein W. Wallace and Tie Cheng Yan. Bounding multi-stage stochastic programs from above. Math. Programming, 61(1, Ser. A):111–129, 1993. [3975] Stein W. Wallace and William T. Ziemba, editors. Applications of Stochastic Programming, volume 5 of MPS-SIAM Book Series on Optimization. SIAM, 2005.

222 [3976] S.W. Wallace. A two-stage stochastic facility-location problem with time-dependent supply. In Numerical techniques for stochastic optimization, Springer Ser. Comput. Math. 10, 489-513, 1988. [3977] S.W. Wallace. Decision making under uncertainty: Is sensitivity analysis of any use? Operations Research, 48:20–25, 2000. [3978] S.W. Wallace, J. Higle, and S. Sen, editors. Stochastic programming, algorithms and models. Baltzer Science Publishers BV, Amsterdam, 1996. Papers from the IFIP Workshop held in Lille- hammer, January 1994, Ann. Oper. Res. 64 (1996). [3979] S. Travis Waller and Athanasios K. Ziliaskopoulos. On the online shortest path problem with limited arc cost dependencies. Networks, 40(4):216–227, 2002. [3980] Yieh Hei Wan. On the average speed of Lemke’s algorithm for quadratic programming. Math. Programming, 35(2):236–246, 1986. [3981] Zhong Ping Wan. An approximate-exact penalty function method for single stage stochastic programming. Gongcheng Shuxue Xuebao, 13(4):37–42, 1996. [3982] Guangyuan Wang and Zhong Qiao. Linear programming with fuzzy random variable coefficients. Fuzzy Sets Syst. 57, No.3, 295-311, 1993. [3983] Guangyuan Wang and Wenquan Wang. Generalized fuzzy constraint programming. Fuzzy Math. 6, No.1, 1-8, 1986. [3984] I.-J. Wang and E.K.P. Chong. A deterministic analysis of simultaneous perturbation stochastic approximation. In Proceedings of the 30th Conference on Information Sciences and Systems, pages 918–922, 1996. [3985] I.-J. Wang and E.K.P. Chong. A deterministic analysis of stochastic approximation with randomized directions. IEEE Transactions on Automatic Control, 43:1749–1749, 1998. [3986] I.-J. Wang and J.C. Spall. A constrained simultaneous perturbation stochastic approximation algorithm based on penalty functions. In Proceedings of the American Control Conference, pages 393–399, 1999. [3987] J. Wang. Continuity of the feasible solution sets of probabilistic constrained programs. J. Optim. Theory Appl., 63(1):79–89, 1989. [3988] J. Wang. Differentiability of the constraint functions in probabilistic constrained programs. Opti- mization, 20(4):509–515, 1989. [3989] Jin De Wang. An introduction to stochastic programming. Chinese J. Oper. Res., 3(1):22–27, 1984. [3990] Jin De Wang. Distribution sensitivity analysis for stochastic programs with complete recourse. Math. Programming, 31(3):286–297, 1985. [3991] Jin De Wang. An approximate method for solving chance-constrained programming problems. Chinese J. Oper. Res., 5(2):67–68, 1986. [3992] Jin De Wang. Lipschitz continuity of objective functions in stochastic programs with fixed recourse and its applications. Math. Programming Stud., 27:145–152, 1986. Stochastic programming 84. I. [3993] Jin De Wang. Stability of stochastic programming with probabilistic constraints. Nanjing Daxue Xuebao Shuxue Bannian Kan, 3(2):177–185, 1986. [3994] Jin De Wang. The sufficient optimality condition for a class of mathematical programs and its application to stochastic programming. Acta Math. Appl. Sinica, 9(2):138–145, 1986. [3995] Jin De Wang. Stability of the optimum of stochastic linear programs. Nanjing Daxue Xuebao Shuxue Bannian Kan, 4(2):109–116, 1987.

223 [3996] Jin De Wang. Approximate nonlinear programming algorithms for solving stochastic programs with recourse. Ann. Oper. Res., 31(1-4):371–384, 1991. Stochastic programming, Part II (Ann Arbor, MI, 1989). [3997] Jin De Wang. Differential stability of the objective functions of stochastic linear programs. Acta Math. Appl. Sinica, 14(4):484–490, 1991. [3998] Jin De Wang. Stability in distribution problems of nonlinear stochastic programming. Asia-Paciﬁc J. Oper. Res., 8(2):128–134, 1991. [3999] Jin De Wang. Stability of multistage stochastic programming. Ann. Oper. Res., 56:313–322, 1995. Stochastic programming (Udine, 1992). [4000] Jin De Wang. A successive approximation method for solving probabilistic constrained programs. Acta Math. Appl. Sinica (English Ser.), 11(1):51–58, 1995. [4001] Jinde Wang. Stochastic Programming. Chinese Presses, Beijing, 1990. (in Chinese). [4002] Jinde Wang. Statistical inference for stochastic programming. Pac. J. Optim., 1(1):179–190, 2005. [4003] L. Wang and J. Wang. Limit distribution of statistical estimators for stochastic programs with dependent samples. ZAMM Z. Angew. Math. Mech., 79(4):257–266, 1999. [4004] Lihong Wang. Asymptotics of statistical estimates in stochastic programming problems with long- range dependent samples. Math. Methods Oper. Res., 55(1):37–54, 2002. [4005] Ling Wang and Liang Zhang. Stochastic optimization using simulated annealing with hypothesis test. Appl. Math. Comput., 174(2):1329–1342, 2006. [4006] P. Patrick Wang and Der-San Chen. Continuous optimization by a variant of simulated annealing. Comput. Optim. Appl., 6(1):59–71, 1996. [4007] Qian Wang, Rajan Batta, and Christopher M. Rump. Algorithms for a facility location problem with stochastic customer demand and immobile servers. Ann. Oper. Res., 111:17–34, 2002. Recent developments in the theory and applications of location models, Part II. [4008] S.-M. Wang, J.-C. Chen, H.-M. Wee, and K.-J. Wang. Non-linear stochastic optimization using genetic algorithm for portfolio selection. Int. J. Oper. Res. (Taichung), 3(1):16–22, 2006. [4009] Ying Ming Wang and Guo Wei Fu. Generalized least deviation methods for deciding priority of comparison matrices in the analytic hierarchy process. J. Tsinghua Univ., 33(3):10–17, 1993. [4010] Y. Wardi. A stochastic algorithm using one sample point per iteration and diminishing stepsizes. J. Optim. Theory Appl., 61(3):473–485, 1989. [4011] Y. Wardi. On a proof of a Robbins-Monro algorithm. Addendum to: ‘A stochastic algorithm using one sample point per iteration and diminishing stepsizes’ [J. Optim. Theory Appl. 61 (1989), no. J. Optim. Theory Appl., 64(1):217, 1990. [4012] Y. Wardi. Stochastic algorithms with Armijo stepsizes for minimization of functions. J. Optim. Theory Appl., 64(2):399–417, 1990. [4013] Y. Wardi. Stochastic approximation algorithm for minimax problems. J. Optim. Theory Appl., 64(3):615–640, 1990. [4014] Manfred K. Warmuth and Dima Kuzmin. Online variance minimization. In Learning theory, volume 4005 of Lecture Notes in Comput. Sci., pages 514–528. Springer, Berlin, 2006. [4015] Tsunemi Watanabe and Hugh Ellis. Robustness in stochastic programming models. Appl. Math. Modelling, 17(10):547–554, 1993.

224 [4016] Tsunemi Watanabe and Hugh Ellis. A joint chance-constrained programming model with row dependence. Eur. J. Oper. Res. 77, No.2, 325-343, 1994. [4017] D.W. Watkins, Jr., D.C. McKinney, and D.P. Morton. Groundwater pollution control. In S.W. Wallace and W.T. Ziemba, editors, Applications of Stochastic Programming, pages 409–424. MPS- SIAM Series on Optimization, 2005. [4018] D.W. Watkins, Jr., D.P. Morton, and D.C. McKinney. Monte carlo techniques for estimating solution quality in stochastic groundwater management models. In Proceedings of the XII International Conference on Computational Methods in Water Resources, Crete, pages 67–74, 1998. [4019] R.R. Weber. Optimal search for a randomly moving object. J. Appl. Probab., 23(3):708–717, 1986. [4020] T.M. Webster. Some experience with stochastic approximation algorithms in large-scale systems. In Proceedings of the American Statistical Association, Statistical Computing Section, pages 181– 186, 1988. [4021] Zeng Xin Wei and Jiang Tao Mo. A new numerical method for stochastic programming with recourse. Chinese Ann. Math. Ser. A, 23(5):601–610, 2002. [4022] Andres´ Weintraub and Jorge Vera. A cutting plane approach for chance constrained linear programs. Oper. Res., 39(5):776–785, 1991. [4023] Joel Weisman and A.G. Holzman. Engineering design optimization under risk. Management Sci., Theory 19, 235-249, 1972. [4024] Gideon Weiss. Stochastic bounds on distributions of optimal value functions with applications to PERT, network flows and realiability. Oper. Res. 34, 595-605, 1986. [4025] D.J.A. Welsh. Stochastic optimization on networks. Oper. Res. Verfahren 32, 203-206, 1979. [4026] M. Werner. Bemerkungen zur zweistufigen stochastischen Programmierung bei Unsicherheit ueber die Verteilung der Zufallsvariablen. In Operations Res.-Verf. 15, 171-173, 1973. [4027] M. Werner. Ein Losungsansatz¨ fur¨ ein spezielles zweistufiges stochastisches Optimierungsproblem. Z. Operations Res. Ser. A-B, 17(3):A119–A128, 1973. [4028] Michael Werner. Stochastische lineare Optimierungsmodelle. Akademische Verlagsgesellschaft, Frankfurt am Main, 1973. Studienbuch fur¨ Studierende der Mathematik, der Wirtschafts- und Sozialwissenschaften sowie aller Ingenieur- und Naturwissenschaften ab 3. oder 4. Semester, Mit einem Vorwort von Hans Hermann Weber. [4029] R. Wernsdorf. Anwendungen der linearen parametrischen Optimierung unter Beruecksichtigung rechentechnischer Aspekte. Wiss. Z. Tech. Hochsch. Ilmenau 28, No.5, 179-188, 1982. [4030] Ralph Wernsdorf. On the connectedness of the set of efficient points in convex optimization problems with multiple or random objectives. Math. Operationsforsch. Stat., Ser. Optimization 15, 379-387, 1984. [4031] R. Wets. Stochastic programming: solution techniques and approximation. In Mathematical programming: the state of the art (Bonn, 1982), pages 566–603. Springer, Berlin, 1983. [4032] R. Wets and Yu. M. Ermol’ev. Problems in stochastic optimization. In Systems research (Russian), pages 45–61, Moscow, 1988. “Nauka”. [4033] R. J.-B. Wets and W. T. Ziemba, editors. Stochastic programming. State of the art. 1998. Baltzer Science Publishers BV, Bussum, 1999. Papers from the 8th International Conference on Stochastic Programming held at the University of British Columbia, Vancouver, BC, August 8–16, 1998, Ann. Oper. Res. 85 (1999).

225 [4034] R.J-B. Wets. Programming under uncertainty: The complete problem. Z. Wahrscheinlichkeitsthe- orie und verw. Gebiete, 4:316–339, 1966. [4035] R.J.-B. Wets. Large scale linear programming techniques. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math., pages 65–93. Springer, Berlin, 1988. [4036] R.J-B. Wets. Laws of large numbers for random lsc functions. Applied Stochastic Analysis and Stochastics Monographs, 5:101–120, 1991. [4037] R.J.-B. Wets. Challenges in stochastic programming. Mathematical Programming, 75(2):115–135, 1996. [4038] Roger Wets. Characterization theorems for stochastic programs. Math. Programming, 2:166–175, 1972. [4039] Roger Wets. Stochastic programs with recourse: A basic theorem for multistage problems. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 21:201–206, 1972. [4040] Roger Wets. Duality relations in stochastic programming. In Symposia Mathematica, Vol. XIX (Convegno sulla Programmazione Matematica e sue Applicazioni, INDAM, Rome, 1974), pages 341–355, London, 1976. Academic Press. [4041] Roger J.-B. Wets. Stochastic programs with ﬁxed recourse: the equivalent deterministic program. SIAM Rev., 16:309–339, 1974. [4042] Roger J.-B. Wets. On the relation between stochastic and deterministic optimization. In Control Theory, numer. Meth., Computer Syst. Mod.; internat. Symp. Rocquencourt 1974, Lecture Notes Econ. math. Syst. 107, 350-361, 1975. [4043] Roger J.-B. Wets. The distribution problem and its relation to other problems in stochastic programming. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 245–262. Academic Press, London, 1980. [4044] Roger J.-B. Wets. Stochastic multipliers, induced feasibility and nonanticipativity in stochastic programming. In Stochastic programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974), pages 137–146, London, 1980. Academic Press. [4045] Roger J.-B. Wets. Solving stochastic programs with simple recourse. Stochastics, 10(3-4):219–242, 1983. [4046] Roger J.-B. Wets. Modeling and solution strategies for unconstrained stochastic optimization problems. In Stochastics and optimization, Sel. Pap. ISSO Meet., Gorguano/Italy 1982, Ann. Oper. Res. 1, 3-22, 1984. [4047] Roger J.-B. Wets. On a compactness theorem for epiconvergent sequences of functions. In Mathe- matical programming (Rio de Janeiro, 1981), pages 347–355. North-Holland, Amsterdam, 1984. [4048] Roger J.-B. Wets. Algorithmic procedures for stochastic optimization. In Computational mathematical programming (Bad Windsheim, 1984), volume 15 of NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci., pages 309–322. Springer, Berlin, 1985. [4049] Roger J.-B. Wets. The aggregation principle in scenario analysis and stochastic optimization. In Algorithms and model formulations in mathematical programming (Bergen, 1987), volume 51 of NATO Adv. Sci. Inst. Ser. F: Comput. Systems Sci., pages 91–113, Berlin, 1989. Springer. [4050] Roger J.-B. Wets. Stochastic programming. In Optimization, volume 1 of Handbooks Oper. Res. Management Sci., pages 573–629. North-Holland, Amsterdam, 1989. [4051] Roger J.-B. Wets. Constrained estimation: consistency and asymptotics. Appl. Stochastic Models Data Anal., 7(1):17–32, 1991.

226 [4052] Roger J.-B. Wets. Stochastic programs with chance constraints: generalized convexity and approximation issues. In Generalized convexity, generalized monotonicity: recent results (Luminy, 1996), pages 61–74. Kluwer Acad. Publ., Dordrecht, 1998. [4053] Roger J.-B. Wets. Statistical estimation from an optimization viewpoint. Ann. Oper. Res., 85:79– 101, 1999. Stochastic programming. State of the art, 1998 (Vancouver, BC). [4054] A. Whinston. Decentralizability of a stochastic optimization approach to water resource allocation. In Inventory Control Water Storage, Conf., Gyoer 1971, Colloqu. math. Soc. Janos Bolyai 7, 335- 350, 1973. [4055] Chelsea C. White. Cost equality and inequality results for a partially observed stochastic optimization problem. IEEE Trans. Systems Man Cybernetics SMC-5, 576-582, 1975. [4056] Chelsea C. White. Procedures for the solution of a ﬁnite-horizon, partially observed, semi- Markov optimization problem. Operations Res. 24, 348-358, 1976. [4057] D.J. White. Dynamic programming and probabilistic constraints. Operations Res. 22, 654-664, 1974. [4058] D.J. White. A min-max-max-min approach to solving a stochastic programming problem with simple recourse. Manage. Sci. 38, No.4, 540-554, 1992. [4059] Charles H. Whiteman. Analytical policy design under rational expectations. Econometrica, 54(6):1387–1405, 1986. [4060] Mary Whiteside, Mark Eakin, Byong Choi, and Henry D. Crockett. Modiﬁed chance constrained linear programming under uncertainty. J. Statist. Comput. Simulation, 67(3):255–287, 2000. [4061] J.E. Whitney, K. Duncan, M. Richardson, and I. Bankman. Parameter estimation in a highly nonlinear model using Simultaneous Perturbation Stochastic Approximation. Communications in Statis- tics – Theory and Methods, 29:1247–1256, 2000. [4062] Peter Whittle. Optimization over time., volume Volume I: Dynamic programming and stochastic control. of Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. Chichester etc.: John Wiley & Sons., 1982. [4063] R. Wiebking. Stochastische Modelle zur optimalen Lastverteilung in einem Kraftwerksverbund. Z. Operat. Res., Ser. B 21, B197-B217, 1977. [4064] Rolf D. Wiebking. Optimal engineering design under uncertainty by geometric programming. Management Sci. 23, 644-651, 1977. [4065] Robert Wieczorkowski. Stochastic algorithms in discrete optimization with noisy values for the function. Mat. Stos., 38:119–153, 1995. [4066] S.T. Wierzchon. Linear programming with fuzzy sets: A general approach. Math. Modelling 9, 447-459, 1987. [4067] S.T. Wierzchon. Randomness and fuzziness in a linear programming problem. In Combining, fuzzy imprecision with probabilistic uncertainty in decision making, Lect. Notes Econ. Math. Syst. 310, 227-239, 1988. [4068] A.G. Wilson. Linear programming and entropy maximizing models. Research memorandum. rm- 74-6., Laxenburg, Austria: IIASA - International Institute for Applied Systems Analysis., 1974. [4069] Dan Wilson. A mean cost approximation for transportation problems with stochastic demand. Naval Res. Logist. Quart. 22, 181-187, 1975.

227 [4070] William E. Winkler. On Dykstra’s iterative fitting procedure. Ann. Probab., 18(3):1410–1415, 1990. [4071] Wayne L. Winston. Operations research applications and algorithms. 2nd. ed. Thomson Informa- tion/Publishing Group, Boston., 1991. [4072] P. Witten and H.-G. Zimmermann. Stochastische Transportprobleme. Z. Operations Res. Ser. A-B, 22(1):A55–A68, 1978. [4073] H. Wolf. Die Ermittlung effizienter Losungen¨ zur stochastischen linearen Optimierungsaufgabe. OR Spektrum, 7(2):81–90, 1985. [4074] Hartmut Wolf. Entscheidungsfindung bei der stochastischen linearen Optimierung durch Entschei- dungsmodelle mit mehrfacher Zielsetzung, volume 84 of Mathematical Systems in Economics. Ver- lagsgruppe Athenaum/Hain/Hanstein,¨ Konigstein/Ts.,¨ 1983. [4075] Richard D. Wollmer. Investment in stochastic minimum cost generalized multicommodity networks with application to coal transport. Networks, 10(4):351–362, 1980. [4076] Richard D. Wollmer. Two-stage linear programming under uncertainty with 0−1 integer first stage variables. Math. Programming, 19(3):279–288, 1980. [4077] Richard D. Wollmer. Critical path planning under uncertainty. Math. Program. Study 25, 164-171, 1985. [4078] Richard D. Wollmer. Investments in stochastic maximum flow networks. Ann. Oper. Res., 31(1- 4):459–467, 1991. Stochastic programming, Part II (Ann Arbor, MI, 1989). [4079] David H. Wolpert, Charlie E. M. Strauss, and Dev Rajnarayan. Advances in distributed optimization using probability collectives. Adv. Complex Syst., 9(4):383–436, 2006. [4080] Eugene Wong. Neural computing and stochastic optimization. In Future tendencies in computer science, control and applied mathematics (Paris, 1992), volume 653 of Lecture Notes in Comput. Sci., pages 339–342. Springer, Berlin, 1992. [4081] G. R. Wood, D. L. J. Alexander, and D. W. Bulger. Approximation of the distribution of convergence times for stochastic global optimisation. J. Global Optim., 22(1-4):271–284, 2002. Dedi- cated to Professor Reiner Horst on his 60th birthday. [4082] G. R. Wood, Z. B. Zabinsky, and B. P. Kristinsdottir. Hesitant adaptive search: the distribution of the number of iterations to convergence. Math. Program., 89(3, Ser. A):479–486, 2001. [4083] G.R. Wood. On computing the dispersion function. J. Optim. Theory Appl., 58(2):331–350, 1988. [4084] G.R. Wood and B.P. Zhang. Estimation of the Lipschitz constant of a function. J. Global Optim., 8(1):91–103, 1996. [4085] Graham R. Wood and Zelda B. Zabinsky. Stochastic adaptive search. In Handbook of global optimization, Vol. 2, volume 62 of Nonconvex Optim. Appl., pages 231–249. Kluwer Acad. Publ., Dordrecht, 2002. [4086] David L. Woodruff, editor. Advances in computational and stochastic optimization, logic programming, and heuristic search. Kluwer Academic Publishers, Boston, MA, 1998. Interfaces in computer science and operations research. [4087] S.E. Wright. Primal-dual aggregation and disaggregation for stochastic linear programs. Math. Oper. Res., 19(4):893–908, 1994. [4088] S.J. Wright and J.N. Holt. Algorithms for nonlinear least squares with linear inequality constraints. SIAM J. Sci. Statist. Comput., 6(4):1033–1048, 1985.

228 [4089] Dong Hua Wu, Wei Wen Tian, Wei Huang, and Dao De Gao. A modiﬁed integral level-set method for solving global optimization. J. Shanghai Univ. Nat. Sci., 7(3):221–224, 2001. [4090] Jason Wu and Suvrajeet Sen. A stochastic programming model for currency option hedging. Ann. Oper. Res., 100:227–249 (2001), 2000. Research in stochastic programming (Vancouver, BC, 1998). [4091] Wei Wu and Yuesheng Xu. Deterministic convergence of an online gradient method for neural networks. J. Comput. Appl. Math., 144(1-2):335–347, 2002. [4092] Zhi You Wu. An approximate computational method for single stage stochastic programming. J. Chongqing Norm. Univ. Nat. Sci. Ed., 17(1):23–28, 2000. [4093] Henry P. Wynn and Anatoly A. Zhigljavsky. The theory of search from a statistical viewpoint. Test, 3(2):1–45, 1994. With discussion and a reply by the authors. [4094] You Min Xi and Lei Yang. Probability aggregation in rational group decision-making. Xi’an Jiaotong Daxue Xuebao, 31(suppl. I):110–114, 1997. [4095] Xiaolan Xie. Evaluation and optimization of two-stage continuous transfer lines subject to time- dependent failures. Discrete Event Dyn. Syst., 12(1):109–122, 2002. WODES ’98 (Cagliari). [4096] Cheng Xian Xu and Zhi Ping Chen. A dual gradient method for solving a class of two-stage stochastic programming problems with recourse. Xi’an Jiaotong Daxue Xuebao, 26(2):123–125, 1992. [4097] Chengxian Xu and Zhiping Chen. A nonlinear model of multistage problem with recourse. Math. Appl., 9(3):358–363, 1996. [4098] H. Xu. Stochastic penalty function methods for nonsmooth constrained minimization. J. Optim. Theory Appl., 88(3):709–724, 1996. [4099] Huifu Xu. An implicit programming approach for a class of stochastic mathematical programs with complementarity constraints. SIAM J. Optim., 16(3):670–696 (electronic), 2006. [4100] Jiu Ping Xu and Jun Li. An interactive algorithm for a class of stochastic multi-objective linear- quadratic programming models. J. Systems Sci. Math. Sci., 22(1):96–106, 2002. [4101] Jiuping Xu and Jun Li. A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model. J. Comput. Appl. Math., 146(1):99–113, 2002. Sino-Japan Optimization Meeting (Hong Kong, 2000). [4102] Li Jian Xu, Bai Wu Wan, and Chong Zhao Han. Robustness of a class of stochastic steady-state optimization algorithms. Xi’an Jiaotong Daxue Xuebao, 29(8):17–23, 31, 1995. [4103] Diana Yakowitz. An exact penalty algorithm for recourse-constrained stochastic linear programs. Appl. Math. Comput., 49(1):39–62, 1992. [4104] Diana S. Yakowitz. A regularized stochastic decomposition algorithm for two-stage stochastic linear programs. Comput. Optim. Appl., 3(1):59–81, 1994. [4105] S. Yakowitz and E. Lugosi. Random search in the presence of noise, with application to machine learning. SIAM J. Sci. Stat. Comput. 11, No.4, 702-712, 1990. [4106] Sid Yakowitz. A decision model and methodology for the AIDS epidemic. Appl. Math. Comput. 52, No.1, 149-172, 1992. [4107] Sid Yakowitz. A globally convergent stochastic approximation. SIAM J. Control Optim., 31(1):30– 40, 1993.

229 [4108] Sid Yakowitz, Thusitha Jayawardena, and Shu Li. Theory for automatic learning under partially observed Markov-dependent noise. IEEE Trans. Automat. Control, 37(9):1316–1324, 1992. [4109] Sidney Yakowitz, Pierre L’Ecuyer, and Felisa Vazquez-Abad.´ Global stochastic optimization with low-dispersion point sets. Oper. Res., 48(6):939–950, 2000. [4110] S.J. Yakowitz and Lloyd Fisher. On sequential search for the maximum of an unknown function. J. Math. Anal. Appl., 41:234–259, 1973. [4111] D. Yan and H. Mukai. Optimization algorithm with probabilistic estimation. J. Optim. Theory Appl., 79(2):345–371, 1993. [4112] Di Yan and H. Mukai. Discrete optimization with estimation. In Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1–3 (Tampa, FL, 1989), pages 2463–2468, New York, 1989. IEEE. [4113] Di Yan and H. Mukai. Stochastic discrete optimization. SIAM J. Control Optim., 30(3):594–612, 1992. [4114] H. Yan, G. Yin, and S.X.-C. Lou. Using stochastic optimization to determine threshold values for the control of unreliable manufacturing systems. J. Optim. Theory Appl., 83(3):511–539, 1994. [4115] Tie Cheng Yan. Several new convexity statements in stochastic programming. Numer. Math. J. Chinese Univ., 6(2):181–185, 1984. [4116] Tie Cheng Yan. A ﬁxed-point algorithm with a simple penalty matrix for solving two-stage stochastic programming problems. Numer. Math. J. Chinese Univ., 15(3):240–249, 1993. [4117] Tie Cheng Yan. A class of feasible policies in multistage stochastic programming. J. Systems Engrg., 10(2):41–47, 1995. [4118] Tiecheng Yan. The locating method for solving two-stage simple recourse stochastic programming. Numer. Math., Nanjing 15, No.3, 240-249, 1993. [4119] Dafeng Yang and Stavros A. Zenios. A scalable parallel interior point algorithm for stochastic linear programming and robust optimization. Comput. Optim. Appl., 7(1):143–158, 1997. Compu- tational issues in high performance software for nonlinear optimization (Capri, 1995). [4120] M. S. Yang and L. H. Lee. Ordinal optimization with subset selection rule. J. Optim. Theory Appl., 113(3):597–620, 2002. [4121] Mike S. Yang, Loohay Lee, and Yu-Chi Ho. On stochastic optimization and its applications to manufacturing. In Mathematics of stochastic manufacturing systems (Williamsburg, VA, 1996), volume 33 of Lectures in Appl. Math., pages 317–331. Amer. Math. Soc., Providence, RI, 1997. [4122] Ping Yang. Least controls for a class of constrained linear stochastic systems. Math. Oper. Res., 18(2):275–291, 1993. [4123] Tae-Yong Yang and Hyun-Joon Kim. A study on the extension of fuzzy programming solution method. J. Korean Oper. Res. Manage. Sci. Soc. 11, No.1, 36-43, 1986. [4124] Yaguang Yang. A new approach to uncertain parameter linear programming. Eur. J. Oper. Res. 54, No.1, 95-114, 1991. [4125] Hitoshi Yano and Masatoshi Sakawa. Interactive fuzzy decision making for generalized multiobjective linear fractional programming problems with fuzzy parameters. Fuzzy Sets and Systems, 32(3):245–261, 1989. [4126] Makoto Yano. Comparative statics in dynamic stochastic models. Differential analysis of a stochastic modiﬁed golden rule state in a Banach space. J. Math. Econ. 18, No.2, 169-185, 1989.

230 [4127] O.V. Yashkir. The stochastic quasigradient method in problems of multifrequency nonlinear interaction. Issled. Operatsii i ASU, 23:26–29, 139, 1984. [4128] O.V. Yashkir. The method of stochastic quasigradients in multifrequency problems on nonlinear interaction. Issled. Oper. ASU 23, 26-29, 1984. [4129] A.I. Yastremskii. Stochastic production models. I. Issled. Operatsii i ASU, 12:93–101, 133, 1978. [4130] A.I. Yastremskii. Stochastic production models. II. Marginal correlations. Issled. Operatsii i ASU, 13:105–112, 136, 1979. [4131] A.I. Yastremskii. Stochastic production models. III. A dynamic stochastic model. Issled. Operatsii i ASU, 14:19–27, 133, 1979. [4132] A.I. Yastremskii. Marginal relations for the linear problem of multistage stochastic programming. Cybernetics, 16(2):297–299, 1980. [4133] A.I. Yastremskii. Optimality conditions in stochastic programming. Cybernetics, 16(1):154–158, 1980. [4134] A.I. Yastremskii. Stochastic models of economics and methods of their qualitative analysis. In Mathematical methods for the solution of economic problems, No. 9 (Russian), pages 175–185, Moscow, 1980. “Nauka”. [4135] A.I. Yastremskii. On duality relations and optimality conditions in linear problems of stochastic programming. Kibernetika (Kiev), 1:102–107, 135, 1987. [4136] A.I. Yastremskii. On the dependence of the effectiveness of some stochastic systems on the degree of dispersion of random parameters. Issled. Operatsii i ASU, 35:21–29, 1991. [4137] A.I. Yastremskij. Stochastic models of mathematical economics. Textbook. (Stokhasticheskie modeli matematicheskoj ehkonomiki. Uchebnoe posobie). Kiev: Golovnoe Izdatel’stvo Izdatel’skogo Ob”edineniya ”Vishcha Shkola”., 1983. [4138] A.I. Yastremskij. Stochastic models and methods of optimal planning. In Stochastic optimization, Proc. Int. Conf., Kiev/USSR 1984, Lect. Notes Control Inf. Sci. 81, 602-607, 1986. [4139] A.I. Yastremskij and I.K. Fedorenko. Techniques for solving and analyzing applied stochastic models in economics. Cybernetics 16, 137-144 translation from Kibernetika 1980, No.1, 122-127 (1980)., 1980. [4140] A.I. Yastremskij and L.I. Krasnikova. Some models of optimal distribution of resources in exe- cution of a complex of scientiﬁc and technological tasks. Sov. J. Autom. Inf. Sci. 19, No.5, 80-83 translation from Avtomatika 1986, No.5, 80-83 (1986)., 1986. [4141] A.I. Yastremskij and M.V. Mikhalevich. Stochastic search methods for a most preferable element and their interactive interpretation. Cybernetics 16, 893-898 translation from Kibernetika 1980, No.6, 90-94 (1980)., 1981. [4142] A.I. Yastremskij and N. Uteuliev. Modeling possibilities of two-step and multistep stochastic models. Sov. J. Autom. Inf. Sci. 20, No.3, 70-73 translation from Avtomatika 1987, No.3, 84-88 (1987)., 1987. [4143] Yaudin, D.B. Matematicheskie metody upravleniya v usloviyakh nepolnoi informatsii. “Sovetskoe Radio”, Moscow, 1974. Zadachi i metody stokhasticheskogo programmirovaniya. [Problems and methods of stochastic programming]. [4144] Y. Yavin. Optimal launch conditions: an optimal stochastic control problem. Comput. Math. Appl., 21(6-7):115–126, 1991.

231 [4145] A.V. Yazenin. Fuzzy and stochastic programming. Fuzzy Sets and Systems, 22(1-2):171–180, 1987. [4146] A.V. Yazenin. Linear programming with random fuzzy data. Soviet J. Comput. Systems Sci., 30(3):86–93, 1992. [4147] A.V. Yazenin. Modeling of constraints in problems of possibilistic linear programming. J. Comput. Systems Sci. Internat., 33(4):71–75, 1995. [4148] A.V. Yazenin. On the problem of possibilistic optimization. Fuzzy Sets and Systems, 81(1):133– 140, 1996. Fuzzy optimization. [4149] H. Q. Ye and Z. B. Tang. Partitioned random search for global optimization with sampling cost and discounting factor. J. Optim. Theory Appl., 110(2):445–455, 2001. [4150] Uri Yechiali. A note on a stochastic production-maximizing transportation problem. Naval Res. Logist. Quart. 18, 429-431, 1971. [4151] James R. Yee and Bruce L. Golden. A note on detemining operating strategies for probabilistic vehicle routing. Nav. Res. Logist. Q. 27, 159-163, 1980. [4152] I.I. Yeremin and V.D. Mazurov. Synthesis of nonstationary processes of mathematical programming, containing pattern recognition. In Studies on mathematical programming (Papers, Third Conf. Math. Programming, Matraf´ ured,¨ 1975), volume 1 of Math. Methods Oper. Res., pages 61– 68, Budapest, 1980. Akad. Kiado.´ [4153] Yu. M. Yermol’yev. A general stochastic programming problem. J. Cybernet., 1(4):106–112, 1971. [4154] G. Yin. Stochastic approximation via averaging: The Polyak’s approach revisited. In Simula- tion and optimization, Proc. Int. Workshop Comput. Intensive Methods Simulation Optimization, Laxenburg/Austria 1990, Lect. Notes Econ. Math. Syst. 374, 119-134, 1992. [4155] G. Yin. Rates of convergence for a class of global stochastic optimization algorithms. SIAM J. Optim., 10(1):99–120 (electronic), 1999. [4156] G. Yin. Convergence of a global stochastic optimization algorithm with partial step size restarting. Adv. in Appl. Probab., 32(2):480–498, 2000. [4157] G. Yin and Ishita Gupta. On a continuous time stochastic approximation problem. Acta Appl. Math., 33(1):3–20, 1993. Stochastic optimization. [4158] G. Yin, R. H. Liu, and Q. Zhang. Recursive algorithms for stock liquidation: a stochastic optimization approach. SIAM J. Optim., 13(1):240–263 (electronic), 2002. [4159] G. Yin, H.M. Yan, and S.X.-C. Lou. On a class of stochastic optimization algorithms with applications to manufacturing models. In Model-oriented data analysis (Petrodvorets, 1992), Contrib. Statist., pages 213–226. Physica, Heidelberg, 1993. [4160] G. Yin, Q. Zhang, H. M. Yan, and E. K. Boukas. Random-direction optimization algorithms with applications to threshold controls. J. Optim. Theory Appl., 110(1):211–233, 2001. [4161] George Yin, Gunter¨ Rudolph, and Hans-Paul Schwefel. Establishing connections between evolutionary algorithms and stochastic approximation. Informatica, 6(1):93–117, 1995. [4162] George Yin and Qing Zhang, editors. Recent advances in control and optimization of manufacturing systems, volume 214 of Lecture Notes in Control and Information Sciences. Springer-Verlag London Ltd., London, 1996. [4163] Suk-Hun Yoon and Jose A. Ventura. Minimizing the mean weighted absolute deviation from due dates in lot-streaming ﬂow shop scheduling. Comput. Oper. Res., 29(10):1301–1315, 2002.

232 [4164] Yuji Yoshida. Duality in dynamic fuzzy systems. Fuzzy Sets and Systems, 95(1):53–65, 1998. [4165] Yasunari Yoshitomi, Hiroko Ikenoue, Toshifumi Takeba, and Shigeyuki Tomita. Genetic algorithm in uncertain environments for solving stochastic programming problem. J. Oper. Res. Soc. Japan, 43(2):266–290, 2000. [4166] Zhao Yong You. Convergence theorems of quasi-Picard iteration of a contraction mapping on probabilistic metric spaces. J. Math. Res. Exposition, 1:25–28, 1981. [4167] Zhao Yong You, Cheng Xian Xu, and Zhi Ping Chen. Measurability of optimal values and optimal solutions to nonlinear stochastic programming problems. Xi’an Jiaotong Daxue Xuebao, 27(3):113–119, 1993. [4168] Zhao Yong You, Cheng Xian Xu, and Zhi Ping Chen. A dual parallel algorithm for solving multistage stochastic programming problems with recourse. Numer. Math. J. Chinese Univ., 16(4):321– 331, 1994. [4169] Richard M. Young. Certainty equivalence, first order certainty equivalence, stochastic control, and the covariance structure. Econometrica 43, 421-430, 1975. [4170] Jingyuan Yu, Baozhu Guo, and Guangtian Zhu. The control of the semi-discrete population evolution system. J. Syst. Sci. Math. Sci. 7, 214-219, 1987. [4171] A.D. Yudin. Duality in multistage stochastic programming. Engrg. Cybernetics, 11(6):908–915, 1973. [4172] A.D. Yudin. Descent along coordinates in infinite-dimensional convex programming problems. Engrg. Cybernetics, 12:29–38, 1974. [4173] D.B. Yudin. Stochastische quadratische Programmierung. Izv. Akad. Nauk SSSR. Tekh. Kibern. 1969, No.3, 3-9, 1969. [4174] D.B. Yudin. Mathematical Methods of Management under Incomplete Information. Problems and Methods of Stochastic Programming. Soviet Radio, Moscow, 1974. (in Russian). [4175] D.B. Yudin. Problems and Methods of Stochastic Programming. Soviet Radio, Moscow, 1979. (in Russian). [4176] D.B. Yudin. Construction of decision rules in stochastic programming problems. Avtomat. i Tele- mekh., 11:76–85, 1984. [4177] D.B. Yudin and A.S. Nemirovskij. The efficiency of the randomization of control. Probl. Slucha- jnogo Poiska 7, 22-66, 1978. [4178] D.B. Yudin and E.V. Tsoy. Integer-valued stochastic programming. Engrg. Cybernetics, 12:1–8, 1974. [4179] D.B. Yudin and E.V. Tzoy. Integer stochastic programming. Izvestia AN SSSR, Tekhnicheskaya Kibernetika, 1:3–11, 1974. in Russian. [4180] Hong Yue and Hong Wang. Minimum entropy control of closed-loop tracking errors for dynamic stochastic systems. IEEE Trans. Automat. Control, 48(1):118–122, 2003. [4181] Yan M. Yufik and Thomas B. Sheridan. Hybrid knowledge-based decision aid for operators of large scale systems. Large Scale Syst. 10, 133-146, 1986. [4182] A.A. Yushkevich. Continuous-time Markov decision processes with interventions. Stochastics 9, 235-274, 1983. [4183] A.A. Yushkevich. Bellman inequalities for Markov decision drift processes. In Probability theory and mathematical statistics, Vol. II (Vilnius, 1985), pages 695–701. VNU Sci. Press, Utrecht, 1987.

233 [4184] A.A. Yushkevich. Continuous-time Markov decision processes with interventions. Stochastics, to appear. [4185] Z.B. Zabinsky and B.P. Kristinsdottir. Complexity analysis integrating pure adaptive search (PAS) and pure random search (PRS). In Developments in global optimization (Szeged, 1995), volume 18 of Nonconvex Optim. Appl., pages 171–181. Kluwer Acad. Publ., Dordrecht, 1997. [4186] Zelda B. Zabinsky and Graham R. Wood. Implementation of stochastic adaptive search with hit- and-run as a generator. In Handbook of global optimization, Vol. 2, volume 62 of Nonconvex Optim. Appl., pages 251–273. Kluwer Acad. Publ., Dordrecht, 2002. [4187] Jitka Zackova. A note on deterministic equivalents to stochastic linear programming problems. Z. Wahrscheinlichkeitstheorie verw. Gebiete 14, 264-268, 1970. [4188] Jitka Zˇ aćkovˇ a.´ A note on deterministic equivalents to stochastic linear programming problems. II. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 24:221–227, 1972. [4189] Yu.P. Zajchenko and S.A. Shumilova. Operations research. Collection of problems. Textbook. (Issledovanie operatsij. Sbornik zadach. Uchebnoe posobie). Kiev: Izdatel’stvo pri Kievskom Gosudarstvennom Universitete Izdatel’skogo Ob”edineniya ”Vishcha Shkola”., 1984. [4190] Ju. A. Zak. An application of stochastic programming methods to the solution of certain problems on the optimization of multivariable memoryless objects. In Theory and methods of construction of multivariable control systems (Russian), pages 170–183, 337. Izdat. “Nauka”, Moscow, 1973. [4191] Ju. A. Zak, G.P. Kondrasin,ˇ and A.P. Lenin. A study of algorithms of random search in problems of the optimization of complex systems. In Problems of random search, 2 (Russian), pages 131–149, 156, 221. Izdat. “Zinatne”, Riga, 1973. [4192] Yu. A. Zak and V.N. Yakhno. Sequential optimization algorithms in problems of discrete stochastic programming. Engrg. Cybernetics, 18(1):6–13 (1981), 1980. [4193] Yu. O. Zak. On some problems of optimization of continuous technological processes. Soviet Automat. Control, 1968(6):8–18, 1969. [4194] Golbon Zakeri, Andrew B. Philpott, and David M. Ryan. Inexact cuts in Benders decomposition. SIAM J. Optim., 10(3):643–657 (electronic), 2000. [4195] V.V. Zakharov. Methode der Integralglaettung in multiextremalen und stochastischen Problemen. Izv. Akad. Nauk SSSR, Tekh. Kibern. 1970, No.4, 19-25, 1970. [4196] M.M. Zakhvatkin and S.P. Uryas’ev. A modification of the Arrow-Hurwicz algorithm for search for saddle points. Issled. Operatsii i ASU, 21:16–20, 1983. [4197] L.Ya. Zamanskij and D.M. Giller. Survivability analysis of stochastic graphs. Issled. Oper. ASU 19, 27-30, 1982. [4198] D.K. Zambitskij. Parametric Steiner problem for discrete median metric spaces and its application. Izv. Akad. Nauk Mold. SSR, Ser. Fiz.-Tekh. Mat. Nauk 1989, No.1, 9-14, 1989. [4199] Giovanni M. Zambruno. Stochastic programming in portfolio selection. Oper. Res. Verfahren 35, 577-579, 1979. [4200] V.K. Zavadskii. The use of simplified models in problems of numerical optimization and solution of equations. Avtomat. i Telemekh., 7:4–10, 1996. [4201] S.K. Zavriev. Hybrid penalty and stochastic gradient method for seeking a max-min. U.S.S.R. Comput. Math. Math. Phys. 19, No.2, 58-72 translation from Zh. Vychisl. Mat. Mat. Fiz. 19, 329- 342 (1979)., 1980.

234 [4202] S.K. Zavriev. On ﬁnding stationary points in the problem of searching for a maximin with constraints. Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., 2:48–57, 73, 1980. [4203] S.K. Zavriev. A stochastic method of discrepancies for seeking max-min. U.S.S.R. Comput. Math. Math. Phys. 21, No.3, 54-64 translation from Zh. Vychisl. Mat. Mat. Fiz. 21, 585-594 (1981)., 1981. [4204] S.K. Zavriev and A.G. Perevozchikov. Attraction of trajectories of ﬁnite-difference inclusions and stability of numerical methods of stochastic nonsmooth optimization. Sov. Phys., Dokl. 35, No.8, 709-711 translation from Dokl. Akad. Nauk SSSR 313, No.6, 1373-1376 (1990)., 1990. [4205] S.K. Zavriev and A.G. Perevozchikov. A stochastic quasigradient method for optimization of the parameters of dynamical systems. Kibernetika (Kiev), 4:104–107, 130, 134, 1990. [4206] S.K. Zavriev and A.G. Perevozchikov. The method of generalized stochastic gradient for solving minimax problems with constrained variables. U.S.S.R. Comput. Math. Math. Phys. 30, No.2, 98- 105 translation from Zh. Vychisl. Mat. Mat. Fiz. 30, No.4, 491-500 (1990)., 1990. [4207] S.K. Zavriev and A.G. Perevozchikov. On a formula for computing stochastic generalized gradients. In Software and models of systems analysis (Russian), pages 173–178, 195. Moskov. Gos. Univ., Moscow, 1991. [4208] S.K. Zavriev and A.G. Perevozchikov. A stochastic analogue of the method of feasible directions. Issled. Operatsii i ASU, 37:9–18, 1991. [4209] S.K. Zavriev and A.G. Perevozchikov. Stochastic generalized gradient methods in problems of the design of dynamical systems. Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., 4:47–52, 74, 1992. [4210] M.K. Zavrieva. A Combined Penalty and Stochastic Quasigradient Method for the Search for a Connected Maximin. Soobshcheniya po Prikladnoi Matematike. [Reports in Applied Mathematics]. Akad. Nauk SSSR Vychisl. Tsentr, Moscow, 1989. (in Russian). [4211] A.I. Zdanok.ˇ Relaxation of stochastic optimization algorithms in the absence of noise. Problemy Sluchain. Poiska, 7:106–122, 318, 1978. Adaptation problems in technical systems. [4212] A.I. Zdanok.ˇ Relaxation of stochastic optimization algorithms in the presence of noise. Problemy Sluchain. Poiska, 7:123–134, 318, 1978. Adaptation problems in technical systems. [4213] Zeev Zeitlin. Optimality conditions for the stochastic transportation problem. Internat. J. Math. Ed. Sci. Tech., 14(1):9–14, 1983. [4214] G. Zellmer. Ueber die Stabilitaet der optimalen Loesung linearer Optimierungsaufgaben mit stochastischen Daten. In XV. Int. Wiss. Kolloquium Tech. Hochsch. Ilmenau 1970, Abt. A, 3-8, 1970. [4215] G. Zellmer. Zum Zusammenhang zwischen Problemen mit Wahrscheinlichkeitsbeschraenkungen und Problemen mit Kompensation in der stochastischen linearen Optimierung. In 21. int. wiss. Kolloq.; Ilmenau 1976, Heft 3, 27-29, 1976. [4216] Eitan Zemel. Random binary search: a randomizing algorithm for global optimization in r1. Math. Oper. Res., 11(4):651–662, 1986. [4217] A.A. Zenios and W.T. Ziemba, editors. Financial Modeling, Focused Issue. 1992. Manag. Sci. 38, No. 11. [4218] Stavros A. Zenios. A model for portfolio management with mortgage-backed securities. Ann. Oper. Res., 43(1-4):337–356, 1993. Applied mathematical programming and modelling (Uxbridge, 1991).

235 [4219] V. Zenˇ ´isek.ˇ An optimum seeking procedure for stochastic problems with restrictions. Internat. J. Control (1), 15:513–521, 1972. [4220] V.V. Zenkov and Ju.M. Codikov. Ein Verfahren zur Loesung von Problemen der stochastischen Programmierung. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1973, Nr. 3, 13-15, 1973. [4221] V.V. Zenkov and Yu. M. Tsodikov. A method of solving stochastic programming problems. Engrg. Cybernetics, 11(3):369–371, 1973. [4222] Mihail Zervos. On the epiconvergence of stochastic optimization problems. Math. Oper. Res., 24(2):495–508, 1999. [4223] S.V. Zhak. Semistochastische Methoden zur Loesung von Aufgaben der konvexen Program- mierung. Kibernetika 1968, No.6, 32-37, 1968. [4224] A.X. Zhang and Sy-Ming Guu. Properties of the multiple lot-sizing problem with rigid demands and general yield distributions. Comput. Math. Appl., 33(5):55–65, 1997. [4225] Joyce Li Zhang and K. Ponnambalam. Hydro energy management optimization in a deregulated electricity market. Optim. Eng., 7(1):47–61, 2006. [4226] Ke Bang Zhang and Bing Zhang Huang. A probabilistic objective model for probabilistic constrained programming and its solution. J. Shanghai Jiaotong Univ., 26(1):90–95, 1992. [4227] Ke Bang Zhang and Ying Zhang. The structure and programming of a stochastic method for global optimization. J. Shanghai Jiaotong Univ., 4:80–86, 119, 1986. [4228] Wei-Bin Zhang. Existence of aperiodic time-dependent solutions in optimal growth economy with three sectors. Internat. J. Systems Sci., 20(10):1943–1953, 1989. [4229] Gongyun Zhao. A log-barrier method with Benders decomposition for solving two-stage stochastic linear programs. Math. Program., 90(3, Ser. A):507–536, 2001. [4230] Gongyun Zhao. A Lagrangian dual method with self-concordant barriers for multi-stage stochastic convex programming. Math. Program., 102(1, Ser. A):1–24, 2005. [4231] Ji Chao Zhao. Equilibrium strategies for sealed bids with a .; 1/ probability distribution of the opponents’ valuations. Qufu Shifan Daxue Xuebao Ziran Kexue Ban, 21(5):123–130, 1995. [4232] Jin Zhao. Limit distributions for optimal solutions in stochastic programming. Nanjing Daxue Xuebao Shuxue Bannian Kan, 14(1):154–160, 1997. [4233] Tian Xu Zhao and Hong Tao Li. Continuity of objective functions in stochastic programming. J. Baoji College Arts Sci. Nat. Sci., 17(2):9–12, 1997. [4234] Tian Xu Zhao and Xu Zi Tian. Solving of a kind of stochastic programming by approximation. J. Baoji College Arts Sci. Nat. Sci., 21(1):10–12, 2001. [4235] Yonggan Zhao and William T. Ziemba. Creating synthetic option strategies for asset allocation with transaction costs using multi-period stochastic programming. Stochastic Programming E- Print Series, http://www.speps.org, 1999. [4236] Yonggan Zhao and William T. Ziemba. Determining risk neutral probabilities and optimal portfolio policies in a dynamic investment model with downside risk control in the presence of trading frictions. Stochastic Programming E-Print Series, http://www.speps.org, 2000. [4237] Yonggan Zhao and William T. Ziemba. Mean-variance versus expected utility in dynamic investment analysis. Stochastic Programming E-Print Series, http://www.speps.org, 2000.

236 [4238] Yonggan Zhao and William T. Ziemba. A stochastic programming model using an endogenously determined worst case risk measure for dynamic asset allocation. Math. Program., 89(2, Ser. B):293–309, 2001. Mathematical programming and finance. [4239] Yonggan Zhao and William T. Ziemba. Intertemporal mean-variance efficiency with a markovian state price density. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [4240] Yonggan Zhao and William T. Ziemba. On leland’s option hedging strategy with transaction costs. Stochastic Programming E-Print Series, http://www.speps.org, 2003. [4241] D. Zhargal and S.S. Lebedev. Integer programming problems with imprecisely specified right-hand sides. Ekonom.` i Mat. Metody, 24(3):518–527, 1988. [4242] A.I. Zhdanok. A relaxation of stochastic optimization algorithms under conditions of noise. Probl. Sluchajnogo Poiska 7, 123-134, 1978. [4243] A.I. Zhdanok. Algorithms of random sorting under conditions of noise. Probl. Sluchajnogo Poiska 8, 149-161, 1980. [4244] A.I. Zhdanov. Solution of ill-posed stochastic linear algebraic equations by the regularized maximum likelihood method. Zh. Vychisl. Mat. i Mat. Fiz., 28(9):1420–1425, 1440, 1988. [4245] Anatoly Zhigljavsky. Branch and probability bound methods for global optimization. Informatica, 1(1):125–140, 190, 201, 1990. [4246] Anatoly A. Zhigljavsky. Theory of global random search, volume 65 of Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht, 1991. Translated and revised from the 1985 Russian original by the author, With a foreword by Sergei M. Ermakov. [4247] Anatoly A. Zhigljavsky. Semiparametric statistical inference in global random search. Acta Appl. Math., 33(1):69–88, 1993. Stochastic optimization. [4248] A.A. Zhiglyavskii. Matematicheskaya teoriya global’ nogo sluchainogo poiska. Leningrad. Univ., Leningrad, 1985. [4249] Anatoly Zhigljavsky [A.A. Zhiglyavskii], editor. Stochastic optimization. Kluwer Academic Pub- lishers Group, Dordrecht, 1993. Acta Appl. Math. 33 (1993), no. 1. [4250] A. Zhilinskas. On the multimodal minimization algorithm constructed axiomatically. Methods Oper. Res. 40, 197-200, 1981. [4251] A. Zhilinskas and A. Katkauskajte. On statistical models of global optimization in the presence of noise. Teor. Optim. Reshenij 12, 43-53, 1987. [4252] A. Zhilinskas and E.` Senkene. On the convergence of one-dimensional one-step algorithms of multiextremal optimization in the presence of noise. Litovsk. Mat. Sb., 21(1):41–46, 1981. [4253] A. Zhilinskas and Eh. Senkene. Convergence of one-dimensional one-stage algorithms for multi- extremal optimization in the presence of noise. Lith. Math. J. 21, 12-15, 1981. [4254] A.G. Zhilinskas. Statistical models of multi-extremal functions and the construction of global optimization algorithms. In Optimization: models, methods, solutions (Russian) (Irkutsk, 1989), pages 81–90. “Nauka” Sibirsk. Otdel., Novosibirsk, 1992. [4255] Antanas Zhilinskas. On models of complicated functions under uncertainty. In Information theory, statistical decision functions, random processes, Trans. 9th Prague Conf., Prague 1982, Vol. A, 113-118, 1983. [4256] Antanas Zhilinskas and Aldona Katkauskaite.˙ Statistical models for global optimization in the presence of noise. Teor. Optimal. Reshenii, 12:43–53, 1987.

237 [4257] L.S. Zhitetskii. A recursive algorithm for adaptive control of a static object. Kibernet. i Vychisl. Tekhn., 49:67–74, 99, 1980. [4258] Wei Jun Zhong, Nan Rong Xu, and Sen Fa Chen. A stochastic global optimization algorithm for multi-person and two-level decision problems. J. Systems Engrg., 7(2):20–28, 1992. [4259] Chang Yin Zhou and Guo Ping He. Approximate Lagrange-Newton algorithms for a class of stochastic programming problems. J. Shandong Univ. Sci. Technol. Nat. Sci., 24(2):80–83, 2005. [4260] Chang Yin Zhou, Guo Ping He, and Shu Shan Li. A stochastic-search-based global convergence algorithm for constrained optimization problems. Appl. Math. J. Chinese Univ. Ser. A, 20(2):197– 206, 2005. [4261] Changyin Zhou and Guoping He. An inexact Lagrange-Newton method for stochastic quadratic programs with recourse. Appl. Math. J. Chinese Univ. Ser. B, 19(2):229–238, 2004. [4262] Dao Li Zhu and Zhong Xue Lei. Subconcave functions and a study on convexity with respect to the normal distribution in stochastic chance-constrained programming. J. Shanghai Jiaotong Univ., 24(3):77–81, 1990. [4263] Guidong Zhu, Jonathan F. Bard, and Gang Yu. A two-stage stochastic programming approach for project planning with uncertain activity durations. J. Sched., 10(3):167–180, 2007. [4264] Xin Shu Zhu. Sequential estimation in stochastic programming. Nanjing Daxue Xuebao Shuxue Bannian Kan, 14(1):133–137, 1997. [4265] Yaochen Zhu. On the convergence of sequential number-theoretic method for optimization. Acta Math. Appl. Sinica (English Ser.), 17(4):532–538, 2001. [4266] V.I.Zhukovski and D.T. Dochev. A p1-optimal solution of a multicriterial problem with uncertainty. Godishnik Vissh. Uchebn. Zaved. Prilozhna Mat., 23(1):9–18 (1988), 1987. [4267] V.I.Zhukovski and D.T. Dochev. A p2-optimal solution of a multicriterial problem with uncertainty. Godishnik Vissh. Uchebn. Zaved. Prilozhna Mat., 23(2):27–40 (1988), 1987. [4268] S.V. Zhulenev. Ein Normalmodell in Problemen der stochastischen Programmierung. Akad. Nauk Arm. SSR, Dokl. 50, 268-272, 1970. [4269] S.V. Zhulenev. Duality in stochastic programming problems with a random plan. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1971, No.4, 19-26, 1971. [4270] S.V. Zhulenev. On a method for seeking a global extremum. Engrg. Cybernetics, 12:32–38, 1974. [4271] Corneliu Zidaroiu. Undiscounted random decision systems with complete connections. Revue Roumaine Math. pur. appl. 21, 487-494, 1976. [4272] Ryszard Zielinski. A Monte Carlo estimation of the maximum of a function. Algorytmy 7, 5-7, 1970. [4273] Ryszard Zielinski. Global stochastic approximation: A review of results and some open problems. In Numerical techniques for stochastic systems, Conf. Gargnano/Italy 1979, 379-386, 1980. [4274] Ryszard Zielinski´ and Peter Neumann. Stochastische Verfahren zur Suche nach dem Minimum einer Funktion, volume 16 of Mathematical Research. Akademie-Verlag, Berlin, 1983. [4275] Ryszard Zielinski´ and Peter Neumann. Stochastyczne metody poszukiwania minimum funkcji. Wydawnictwa Naukowo-Techniczne (WNT), Warsaw, 1986. Translated from the German by Zielinski.´ [4276] William T. Ziemba. Duality relations, certainty equivalents and bounds for convex stochastic programs with simple recourse. Cahiers Centre Etudes´ Recherche Oper.´ , 13:85–97, 1971.

238 [4277] William T. Ziemba. Transforming stochastic dynamic programming problems into nonlinear programs. Management Sci., Theory 17, 450-462, 1971. [4278] William T. Ziemba. Stochastic programs with simple recourse. In Mathematical programming in theory and practice (Proc. NATO Adv. Study Inst., Figueira da Foz, 1972), pages 213–273, Amsterdam, 1974. North-Holland. [4279] W.T. Ziemba. Stochastic programming models of dynamic planning problems. Econ. Comput. Econ. Cybern. Stud. Res. 1970, No.3, 67-85, 1970. [4280] W.T. Ziemba. Stochastic programs with simple recourse. In P.L. Hammer and G. Zoutendijk, editors, Mathematical Programming in Theory and Practice, pages 213–273. North-Holland Pub- lishing Company, Amsterdam, 1974. [4281] W.T. Ziemba and J.M. Mulvey, editors. World Wide Asset and Liability Management. Cambridge Univ. Press, 1998. [4282] W.T. Ziemba and R.G. Vickson, editors. Stochastic optimization models in ﬁnance. Academic Press, New York, 1975. [4283] Mynt Zijlstra. Optimization of repair limit replacement policies for one-unit systems. RAIRO Rech. Oper.´ , 15(4):351–361, 1981. [4284] Itzhak Zilcha. Weakly maximal optimal stationary program under uncertainty. Internat. econom. Review 16, 796-799, 1975. [4285] Itzhak Zilcha. Characterization by prices of optimal programs under uncertainty. J. math. Eco- nomics 3, 173-183, 1976. [4286] A. Zilinskas. Optimization of one-dimensional multimodal functions. J. R. Stat. Soc., Ser. C 27, 367-375, 1978. [4287] A. Zilinskas. The use of statistical models for construction of multimodal optimization algorithms. In Information theory, Proc. 3rd Czech.-Sov.-Hung. Semin., Liblice 1980, 219- 224, 1980. [4288] A. Zilinskas.ˇ Two algorithms for one-dimensional multimodal minimization. Math. Operations- forsch. Statist. Ser. Optim., 12(1):53–63, 1981. [4289] A. Zilinskas. Axiomatic approach to statistical models and their use in multimodal optimization theory. Math. Program. 22, 104-116, 1982. [4290] A. Zilinskas. Multimodal minimization algorithm constructed axiomatically: Proof of convergence and testing results. Wiss. Z. Hochsch. Archit. Bauwes. Weimar 28, 226-228, 1982. [4291] A. Zilinskas. On justiﬁcation of use of stochastic functions for multimodal optimization models. In Stochastics and optimization, Sel. Pap. ISSO Meet., Gorguano/Italy 1982, Ann. Oper. Res. 1, 129-134, 1984. [4292] A. Zilinskas.ˇ A review of statistical models for global optimization. J. Global Optim., 2(2):145– 153, 1992. [4293] A. Zilinskasˇ and J. Zilinskas.ˇ Global optimization based on a statistical model and simplicial partitioning. Comput. Math. Appl., 44(7):957–967, 2002. Global optimization, control, and games, IV. [4294] A.G. Zilinskasˇ and I.B. Mockus. A certain Bayesian method of search for the minimum. Avtomat. i Vycisl.ˇ Tehn. (Riga), 4:42–44, 1972. [4295] A.G. Zilinskas,ˇ I.B. Mockus, and L.L. Timofeev. A Bayesian method of extremal search with restricted memory. Avtomat. i Vycisl.ˇ Tehn. (Riga), 6:37–42, 1972.

239 [4296] Antanas Zilinskas. Mimun. Optimization of one-dimensional multimodal functions in the presence of noise. Apl. Mat. 25, 234-240, 1980. [4297] Antanas Zilinskas.ˇ Statistical models of multimodal functions and construction of algorithms for global optimization. Informatica, 1(1):141–155, 191, 202, 1990. [4298] H.-J. Zimmermann. Neuere Entwicklung auf dem Gebiet der stochastischen Programmierung (Ue- bersichtsvortrag). In Proc. Oper. Res. 3, DGOR Ann. Meet. Karlsruhe 1973, 43-60, 1974. [4299] H.-J. Zimmermann. Fuzzy set theory and mathematical programming. In Fuzzy sets theory and applications, Proc. NATO Adv. Study Inst., Louvain- la-Neuve/Belg. 1985, NATO ASI Ser., Ser. C 177, 99-114, 1986. [4300] H.-J. Zimmermann and M.A. Pollatschek. The domain of the ”resource-vector” as an aid to decision making in stochastic 0/1 programming. In Operations Res.-Verf. 14, 390-398, 1972. [4301] H.-J. Zimmermann and M.A. Pollatschek. On stochastic integer programming. Z. Operations Res. Ser. A-B, 19:A37–A48, 1975. [4302] H.-J. Zimmermann and M.A. Pollatschek. The probability distribution function of the optimum of a 0 − 1 linear program with randomly distributed coefﬁcients of the objective function and the right-hand side. Operations Res., 23(1):137–149, 1975. [4303] Hans-Juergen Zimmermann. Methoden und Modelle des Operations Research. Fuer Inge- nieure, Oekonomen und Informatiker. (Methods and models of operations research. For engineers, economists and computer scientists). Rechnerorientierte Ingenieurmathematik. Braun- schweig/Wiesbaden: Friedr. Vieweg & Sohn. XIV, 364 S., 1987. [4304] Mincho P. Zlatev. Optimization analysis. A principled synthesized generalization. Problemi Tekhn. Kibernet. Robot., 20:12–27, 1984. [4305] M.A. Zohdy, M.S. Fadali, and J. Liu. Robust design of discrete-time systems via optimization. Internat. J. Systems Sci., 24(4):797–803, 1993. [4306] S.V. Zulenev.ˇ A normal model in stochastic programming problems. A special case. In Mathe- matical methods for the solution of economic problems (Suppl. to Ekonom.` i Mat. Metody), No. 3 (Russian), pages 59–68. Izdat. “Nauka”, Moscow, 1972. [4307] S.V. Zulenev. Ueber eine Methode zum Suchen eines globalen Extremums. Izv. Akad. Nauk SSSR, tehn. Kibernet. 1974, Nr. 2, 46-52, 1974.

240