75 o N o PTIMA Mathematical Programming Society Newsletter December 2007 Rapid Development of an Open-source Minlp Solver with COIN-OR Pierre Bonami, John J. Forrest, Jon Lee and Andreas Wächter Abstract • Csdp, Dfo, Ipopt, LaGO, and Svm- QP are solvers for different types of We describe the rapid development of Nonlinear Optimization (semidefinite, Bonmin (Basic Open-source Nonlinear derivative-free, general large-scale Mixed ) using the interior point, global optimization, QP community and components of COIN- solver for support vector machines) OR (COmputational INfrastructure • CoinMP, FlopC++, GAMSlinks, for Operations Research). NLPAPI, Osi, OS and Smi are problem 1. Introduction modeling and interface tools. Even more, COIN-OR has become the As famous examples like Linux have platform that facilitates the collaboration proven, open-source communities of optimization researchers to start entirely can produce rapidly-developing high- new projects, exploring and developing new quality software, often competitive with algorithmic ideas, by providing both a sound expensive commercial solutions. COIN- software basis that can be re-used, as well as OR (COmputational INfrastructure the technical forum to coordinate the effort. for Operations Research), originally In order to clarify a common founded by IBM in 2000 and a non-profit misconception, we want to emphasize that foundation since 2004, provides such the term “open source” does not simply refer a platform for us optimization folks. to software that is made available to some Since its conception, a number of users in source-code format. According optimization-algorithm implementations to the definition put forth by the non- and related software projects have been profit corporation Open Source Initiative contributed to COIN-OR. From a web (OSI) [26], a number of conditions must server hosted by INFORMS, at the URL be met for a software license to be an www.COIN-OR.org, COIN-OR offers “open-source” license, including the right online repositories for sharing source code, for free distribution and usage (including web sites with information, documentation for commercial purposes), as well as the and bug tracking systems, as well as mailing right to modify the code. There are many lists for users and developers. Many of OSI-certified open-source licenses. The the optimization codes have been used one preferred on COIN-OR is the CPL extensively by academics and in commercial (Common Public License [12]), which was products. chosen for its very liberal terms. Currently, COIN-OR hosts many In this article, we tell the on-going success optimization-related codes: story of one such project. In 2004, IBM and • Clp, DyLP, and Vol are solvers Carnegie Mellon University initiated a joint for study aimed at Mixed Integer Nonlinear • Bcp, Cbc, Cgl, Cops, and Symphony Programming (MINLP), with the goal of are solvers, frameworks and tools releasing the resulting software under the for (serial and parallel) Mixed- CPL on COIN-OR. In 2006, within a Integer Linear Programming, new Open Collaborative Research (OCR) 

75George Nemhauser's Contributions 5 MPS Chair’s Optima Column 6 Prizes and Conferences 7 o p t i m a 7 5 December 2007 page 

initiative at IBM, this relationship with g(x) ≤ 0, sub-domain, problems can be much harder CMU was extended. This OCR program x ∈ Rn-k × Zk, than the MILP counterparts. A main reason builds on the Open Collaboration Principles where f : Rn a R and g : Rn a Rm are is that in the space of the natural variables, established in 2005 by IBM and eleven twice continuously differentiable. the solution of a relaxation may be well other institutions to accelerate innovation MINLP is the mother of all deterministic inside the interior of the feasible region, and foster open-source research. optimization problems. Many business and so the cutting planes that have been so Besides the joint activity of CMU and and engineering optimization problems successful for MILP may have very limited IBM, the subject of MINLP has received a are naturally formulated as mathematical value (see [24], for example). lot of recent attention. For example, programs involving both discrete and If the relaxation of the MINLP problem • The 2006 Beale-Orchard Hays Prize continuous variables, as often decisions is not convex, we are really in a different for Excellence in Computational have to be made that involve making world. There are several approaches. There Mathematical Programming was discrete decisions (e.g., yes/no) and setting are ad hoc heuristics, which suffer from awarded by the Mathematical continuous levels (e.g., flowrates). Natural being well suited to only very specific Programming Society to Nick Sahinidis phenomena often involve relationships models (see [23], for example). There is the and Mohit Tawarmalani for their between variables which, while often possibility of taking methods designed for work on global optimization which smooth, may be rather nonlinear. Accurate problems having convex relaxations and culminated in their software Baron [3, models need to allow for all of these. heuristically adapting them to problems 27]; global optimization is one of the key A common approach to such problems that do not satisfy this restriction (e.g., approaches to MINLP, and Baron can is to reformulate them as Mixed Integer the branch-and-bound option of Bonmin; be directly applied to MINLP problems. Linear Programming (MILP) problems, see [7]). There is the approach of global • The 2006 CORE Lecture Series usually through the use of piecewise-linear optimization typified by the method of consisted of a series of lectures by functions approximating the true functions. spatial branch-and-bound wherein one Robert Weismantel on MINLP. In the presence of non-convexity, this leads repeatedly subdivides the feasible region, Our goal was to develop algorithms to the introduction of additional binary with the goal of producing better and and software for this important class of variables or non-standard branching rules. better convex under-estimators (e.g., Baron; problems. We undertook to carry this out in The inaccuracies that are introduced and see [28]). Finally, there is the approach of the context of COIN-OR. Our original goal the added computational effort induced systematically remodeling a broad subclass was to use existing software components of by accommodating the piecewise-linear of MINLP problems as MILPs using COIN-OR to produce a simple NLP-based functions may make the value of such a specialized techniques (e.g., see [16] for such branch-and-bound code aimed at MINLP solution approach rather limited. a method using linked ordered sets) problems that have convex relaxations. As Another approach is to relax the MINLP we progressed, we expanded our goal and to an NLP, apply an NLP solver, and then 3. Building Blocks developed instantiations of several MINLP use some heuristic method to reach a nearby As MINLP combines the worlds of methods, aimed mostly at problems having feasible point that respects the integrality MILP and of NLP, a logical start for convex relaxations. We were able to carry restrictions. Just as for MILP, this technique the Bonmin project was to look at the this out rather quickly, as we had at our is not very robust, often leading to very poor existing codes and libraries in COIN- disposal the source code to manage a solutions. OR related to MILP and NLP and to branch-and-bound tree and to solve MILP The alternative to methods that are based see how they could be integrated. and NLP subproblems. strictly on either MILP and NLP is to Cbc (Coin Branch and Cut) is a powerful, In Section 2, we describe the setting develop methods that are directly aimed at industrial-strength branch-and-cut code of MINLP. In Section 3, we discuss the MINLP formulations. In effect, one shifts for MILP problems. It is a component COIN-OR NLP solver Ipopt and the some of the burden from the modeler to of COIN-OR, and it uses several other COIN-OR MILP solver Cbc, which were the solution software. Still, just as we know components of COIN-OR. It uses Clp (the the starting points of our implementation. from MILP and NLP, there are always Coin Linear Programming solver) through In Section 4, we describe the capabilities significant issues that cannot be ignored the Osi (Open Solver Interface) library. The of our MINLP solver Bonmin (Basic by a modeler who seeks to solve difficult Osi is a layer used to insulate an application Open-source Nonlinear Mixed INteger instances. that makes use of an LP solver from the programming) and how we constructed It is useful to first consider methods specific LP solver employed. Clp includes it using other components of COIN-OR. that are aimed at MINLP problems primal and dual simplex solvers as well as Finally, in Section 5, we discuss ongoing having convex relaxations. In this sub- an interior-point method. As a full-fledged and future plans for Bonmin. domain, there are natural methods that branch-and-cut code, Cbc strengthens generalize MILP methods (e.g., branch- relaxations through use of the COIN Cgl 2. MINLP and-bound, using NLP subproblems) as (Cut Generation Library), accommodates well as more sophisticated methods like We consider MINLP problems of the form different node-selection and branching rules outer approximation (see [13]), generalized min f(x) (e.g., via pseudocosts and strong branching), Bender's decomposition (see [18]) and hybrid and allows for SOS Type-1 and Type-2 methods (see [8], for example). Even in this Date: November 2, 2007. modeling and branching. Cgl includes a o p t i m a 7 5 December 2007 page 

wide variety of cutting-plane generators (including: knapsack cover, odd hole, flow cover, lift and project, Gomory, reduce and split, and MIR). Our interest in Cbc was twofold. We sought to re-use infrastructure that we would need (for example, maintaining any needed branch-and-bound enumeration trees, handling the branching and fathoming decisions, etc.), but we also simply wanted the Cbc functionality for solving any MILP subproblems that we might create. To address the nonlinear aspect of the problem, the Ipopt NLP solver from COIN-OR was used. Ipopt implements an algorithm for continuous nonlinear optimization (see [29]). Its interior point approach, together with a third-party sparse linear algebra routine such as MA27 [20], Figure 1. Code re-use by Bonmin and growth allows Ipopt to efficiently solve large-scale problems with up to millions of variables. organize a branch-and-bound search, The success of the project is facilitated Global convergence (i.e.,convergence where now all the nodes are NLPs. The by the fact that all essential components to a stationary point from any starting nonlinear relaxations are solved by Ipopt, were available as open-source code, so point) is achieved by a filter line-search which has been connected to Cbc via an that they could be changed (and changes procedure. Here, nonconvexities in the Osi solver object. Attempts were also made could be contributed back to the project problem formulation are tackled by possibly to handle nonconvex problem instances maintainers), and by the object-oriented regularizing the Hessian matrix of the by some heuristics, such as negative cut- design of the codes. Figure 1 indicates how Lagrangian to ensure that the search off, multiple local optimization runs for Bonmin makes significant re-use of COIN- directions are descent directions in the the node NLPs from randomly chosen OR components. The ordinate indicates appropriate sense, so that convergence to starting points, and continuing branching the number of lines of code for the various non-minimizers is less likely. Since Ipopt even at (locally) infeasible nodes. The components. In the totals, we do not count is using second derivatives, fast local integration of these features, which helped parts of some codes that we definitively convergence can be achieved. However, if to obtain better solutions, would not have do not use. The bar for Bonmin refers to second derivatives are not available, they are been possible if the source code of the the new code written specifically for the approximated by a quasi-Newton approach. components had not have been available. MINLP project. Besides demonstrating The Ipopt code was originally written in Another popular strategy for solving how Bonmin is re-using COIN-OR Fortran, but a complete rewrite in C++, convex MINLPs uses Outer Approximation components, Figure 1 also indicates how all following an object-oriented approach, was (OA). The basic idea is to approximate the of these components (including Bonmin) are released on COIN-OR in 2004. The Ipopt original nonlinear problem by a sequence growing. For each component, we indicate library includes a few utility functionalities, of MILPs, where, successively, linear cuts the number of (relevant) lines of code as of such as output logging and algorithmic are added based on linearizations of the the most-recent stable release on COIN- options handling, which can be used by nonlinear functions. The OA algorithm OR, as well as the current incremental size other codes as well. alternatingly solves the current MILP (as of 21 May, 2007) in the \trunk“ (i.e., All of these basic components from approximation and an NLP (the MINLP development branch) of each project. COIN are being actively developed and with all integer variables fixed). It can be Bonmin can be accessed as a C++ library, have a wide user basis. shown that this procedure with appropriate as a stand-alone code that can accept linearization points converges to the optimal an input file in .nl format [17] from the 4. Bonmin solution of the MINLP in a finite number mathematical-programming modeling of iterations (see [13]). Using Cbc with and scripting language Ampl [1], and via Using the building blocks described in Clp as the MILP solver and Ipopt as the the NEOS Server for Optimization [25]. Section 3, we began to develop Bonmin NLP solver, we could implement the OA Similar to Ampl, Gams is another widely (Basic open-source nonlinear mixed algorithm in Bonmin with existing COIN- used scripting and modeling language for integer programming). In the first phase, OR components. manipulating mathematical programs. we sought to implement an MINLP An intermediate hybrid approach between The recently added COIN-OR project, code targeted at problems with convex a pure branch-and-bound and a pure OA GAMSlinks, managed by Stefan Vigerske, relaxations. A straightforward approach algorithm has also been developed and provides an interface to Bonmin (as well as employing available components from implemented in Bonmin [8]. the COIN- OR solvers Ipopt and Cbc). COIN-OR uses the Cbc framework to o p t i m a 7 5 December 2007 page 

5. Ongoing and future work COIN addition LaGO (Lagrangian Global MILP. Already we have some success for Optimizer), authored by Ivo Nowak and structured problems (see [19]) and we are We are presently pursuing several Stefan Vigerske. The LaGO code itself is a currently exploring more generic techniques. initiatives with the goal of extending MINLP solver that makes use of Clp, Cgl, Finally, there are other components of the applicability of our work. and Ipopt, and is based on some heuristics. COIN-OR that we may consider taking One ongoing project involves using the However, for many MINLP instances, advantage of. For example, Csdp (a parallel MILP framework of the COIN- it is impractical to expect to be able to semidefinite-programming code authored by OR code Bcp (Branch-Cut-and Price) to reliably find the global optimum. So, an Brian Borchers) and Dfo (a derivative-free develop a parallel version of Bonmin. Our extremely important area is the development NLP code authored by Katya Scheinberg) goal is to exploit parallelism on a small scale of general-purpose heuristics for MINLP. could be exploited in an attempt to solve as well as on massively parallel architectures Already, in the context of the development broader classes of MINLP problems than we (like BlueGene; see [5]). Alternatively, of the Bonmin project, some success in currently consider. we might consider use of the relatively this direction has been achieved (see [6]). new COIN-OR Cops (COIN-OR Open Still, there is much more work to do in this It is our fondest desire that this entire Parallel Search) framework, to manage the direction. manuscript be already obsolete by the parallelization. The use of object-oriented We are also investigating the use of other time that you are reading this. Indeed, for design for the basic Bonmin code facilitates NLP solvers (e.g., active-set approaches like our project to be succeeding, that should the easy adaption into different search tree that of FilterSQP [14]) as an alternative to or be the case. The very latest information management frameworks (e.g., Cbc, Bcp, in conjunction with Ipopt. concerning our efforts should be available Cops). On the theoretical side, we are exploring from the Bonmin web page [9] and Another project jointly explored with the use of curvature information from the the IBM MINLP web page [21]. Carnegie Mellon University, involves NLP in making branching decisions in the the use of global-optimization ideas and branch-and-bound MINLP frame-work. 6. Acknowledgments software. We are experimenting with the We are already finding this approach to be Thanks are due to the others who usage of rigorous convex under-estimators useful for certain nonlinear facility-location have participated in the CMU/IBM and spatial decomposition. The resulting problems as well as certain portfolio- collaboration, namely Pietro Belotti, Larry software will be available on COIN-OR as optimization problems. Biegler, Andrew Conn, Gérard Cornuéjols, Couenne (Convex Over/Under ENvelopes We are also investigating the Ignacio Grossman, Carl Laird, Andrea for Nonlinear Estimation). Similarly, strengthening of MINLP formulations, Lodi, Françcois Margot and Nick Sawaya. we are exploring the possibility to re-use following the success of such methods for some globalization cuts from the recent

References for convex mixed integer 14. FilterSQP, www-unix.mcs.anl. 21. IBM MINLP, domino.research. nonlinear programs. IBM gov/~leyffer/solvers.html ibm.com/comm/research 1. Ampl, www.ampl.com Research Report RC23771, 15. C.A. Floudas, Deterministic projects.nsf/pages/minlp. 2. Ampl Solver Library, www. October 2005. To appear in: global optimization, Kluwer index.html netlib.org/ampl/solvers Discrete Optimization. Acad. Publ., Dordrecht, 2000. 22. Lapack, www.netlib.org/lapack 3. Baron, archimedes.scs.uiuc.edu/ 9. Bonmin, projects.COIN- 16. J. Forrest and J. Lee (in 23. J. Lee, In situ column baron.html OR.org/Bonmin preparation). generation for a cutting- 4. Blas, www.netlib.org/blas 10. C. Bragalli, C. D'Ambrosio, J. 17. D.M. Gay, Writing .nl files, stock problem. Computers 5. BlueGene, IBM Journal of Lee, A. Lodi and P. Toth, An Technical Report 2005-7907P, & Operations Research, Research and Development, MINLP model and solution Sandia National Laboratories, 34(8):2345-2358, 2007. Volume 49, Number 2/3, method for a water network Albuquerque, NM, 2005. 24. J. Lee, Mixed integer nonlinear 2005. www.research.ibm. optimization problem. In www.cs.sandia.gov/~dmgay/ programming: Some modeling com/journal/rd49-23.html Algorithms - ESA 2006, Y. nlwrite.pdf and solution issues, to appear 6. P. Bonami, G. Cornuéjols, Azar and T. Erlebach, Eds., 18. A.M Geoffrion. Generalized in the IBM Journal of A. Lodi and F. Margot. A pages 696-707. Springer, Benders decomposition. Research and Development, Feasibility Pump for Mixed 2006. Journal of Optimization 2007. Integer Nonlinear Programs. 11. COIN-OR, www.COIN- Theory and Applications, 25. NEOS Server for Optimization, IBM Research Report OR.org 10:237{260, 1972. www-neos.mcs.anl.gov RC23862, 2006. 12. Common Public License, www. 19. O. Günlük, J. Lee and R. 26. Open Source Initiative, www. 7. P. Bonami and J. Lee, BONMIN opensource.org/licenses/ Weismantel. MINLP opensource.org Users' Manual. projects. cpl1.0.php Strengthening for Separable 27. N. Sahinidis and M. COIN-OR.org/Bonmin 13. M. Duran and I.E. Grossmann. Convex Quadratic Tawarmalani, A polyhedral 8. P. Bonami, A. Wächter, L.T. An outer-approximation Transportation-Cost UFL, branch-and-cut approach Biegler, A.R. Conn, G. algorithm for a class of mixed- IBM Research Report to global optimization, Cornuéjols, I.E. Grossmann, integer nonlinear programs. RC24213, March 2007. Mathematical Programming, C.D. Laird, J. Lee, A. Lodi, Mathematical Programming, 20. Harwell Subroutine Library, 103(2), pp. 225-249, 2005. F. Margot and N. Sawaya, 36:307{339, 1986. www.cse.clrc.ac.uk/nag/hsl 28. M. Tawarmalani and N.V. An algorithmic framework Sahinidis, Convexification  o p t i m a 7 5 December 2007 page 

Optimization Research Symposium Recognizing Professor George Nemhauser’s Contributions to the Field of Operations Research July 27, 2007 marked the 70th birthday of George Nemhauser. George has been a long-time member of MPS, served as its president from 1989-1992 and co-chaired the ISMP at in 2000. To mark the occasion of George’s birthday, a two-day symposium was held in his honor at the Georgia Institute of Technology in Atlanta, GA. The symposium included a mix of serious scientific lectures and, sometimes less serious presentations on George’s career and his contributions to various fields and institutions. There were 17 invited speakers and close to 100 attendees. The symposium was organized by Mike Ball and Martin Savelsbergh. The Thursday afternoon program included one session on George’s scientific contributions to four disciplines: integer programming, presented by Bob Bixby, combinatorial optimization presented by Gerard Cornuéjols, airline optimization presented by David Ryan and sports scheduling presented by Mike Trick. A second session covered George’s naming of a prime number in George’s Cutting Planes” by Ralph Gomory, contributions to four institutions: Johns honor by Groetschel. While Gerard “Minimizing with Concave Costs?” by Tom Hopkins University presented by Mike Cornuejols presented George with one Magnanti, and “Integer Programming and Thomas, presented of his integer programming homework Branch-Width” by Bill Cunningham. Each by Dave Goldsman, CORE presented assignments from Cornell, it did come of the speakers has had close ties to George by Lawrence Wolsey and Georgia Tech with the request that George regrade a over the years but more significantly the presented by John Jarvis. There was a special problem he had incorrectly graded 30 years body of results presented had numerous bonus presentation by Martin Grötschel and ago. Although Bob Bixby demonstrated connections to his work. the evening dinner included remarks by Bill that certain mixed integer cuts developed Overall the symposium proved to be Pulleyblank, Don Ratliff and Mike Ball. by Nemhauser and his co-authors were the both intellectually stimulating and, at Several presentations included gifts such basis for a substantial speed improvement times, highly entertaining. By examining as a selection of red and white New Zealand in Cplex, no associated stock options the contributions of a great individual in wines by Ryan and Trick and the official were provided. The institutional this way, one can gain an appreciation for presentations chronicled George’s significant the substantial positive impact one can contributions to four great institutions and have through a career in mathematical and global optimization in continuous and also demonstrated George’s ability both programming. The symposium was mixed-integer nonlinear programming, to solve and create problems. The dinner certainly a fitting tribute to George Kluwer Acad. Publ., Dordrecht, 2002. presentations were lighter in tone and ended Nemhauser for providing such a positive role 29. A. Wächter and L. T. Biegler, On the model to our community. Implementation of an Interior-Point Filter with a presentation of a compilation of the Line-Search Algorithm for Large-Scale title pages and table of contents from the 50 Nonlinear Programming, Mathematical PhD dissertations supervised by George. Michael O. Ball Programming 106(1), pp. 25-57, 2006. The Friday program included five Orkand Corporation Professor scientific presentations: “Retail Assortment of Management Science IBM T.J. Watson Research Center, Optimization” by Marshall Fisher, “Airline Robert H. Smith School of Business Yorktown Heights, New York. USA Optimization: If we are so good at it, why and Institute for Systems Research e-mail address: fpbonami,jjforre,jonlee,a are things so bad?” by Cindy Barnhart, University of Maryland [email protected] “Corner Polyhedra and Two-Equation College Park, MD 20742 o p t i m a 7 5 December 2007 page 

MPS Chair’s Optima Column – 3rd issue of 2007 By Steve Wright

I am delighted to contribute the inaugural a wonderful symposium and witness in the last two congresses, as organizers and MPS Chair’s column for Optima. As the exciting recent changes to this great speakers, and our new status will formalize you can see, Optima is being published American city. and solidify our involvement. on a regular schedule once again. Under We welcome new editors of our Society’s I wish to thank the organizers of several the leadership of editor Andrea Lodi, journal Mathematical Programming: Kurt recent meetings sponsored by MPS in the design of our Society’s newsletter is Anstreicher (Series A) and Danny Ralph 2007. IPCO continued its tradition as a key being reworked, and we look forward to (Series B). The number of published issues meeting of the integer programming and exciting innovations in the months ahead. will increase from nine to ten in 2008 and combinatorial optimization community MPS has recently had a large increase later years, a reflection of the robust health with a highly successful meeting in June at in membership due to the 2006 ISMP in of the journal. As always, subscription to the Cornell. Thanks to David Williamson and Rio de Janeiro and the 2007 ICCOPT in print version of the journal is included in Matteo Fischetti and all involved with the Hamilton. Renewal notices for 2008 have MPS membership. The online version, along organization and selection of papers for this recently gone out. I hope that our new with complete archives of the journal and event. ICCOPT at McMaster University members will stay involved in the Society Mathematical Programming Studies, is also in August was an outstanding success, and help it play an ever more important role free to members. We also welcome Philippe under general chair Tamas Terlaky and in sustaining and building our international Toint, the new editor of the MPS-SIAM his large and excellent cast of organizers. community of optimizers and mathematical book series. Please contact Philippe or one of The 420 attendees enjoyed good weather, programmers. his editorial board members with any book- an excellent venue and program, and a Preparations for the 2009 ISMP in writing ideas you may have. wonderful roster of social events. Chicago gathering momentum under I take this opportunity to remind you of Finally, I thank the officers and general chair John Birge. The symposium the generous discounts available to MPS councilors of MPS whose terms have ended will be held in the week of August 23-28, members on all books published by Springer recently. Former Chair Rolf Möhring 2009, with most sessions taking place at the and SIAM. A new SpringerToken will be continues as Vice-Chair, so we will Gleacher Center (the downtown campus issued in 2008; look for it in your email continue to have the benefit of his wisdom of the University of Chicago Business inbox. and experience. Karen Aardal is stepping School) and the nearby Marriot Hotel. Another snippet of news is that down as Chair of the Executive Committee. Both locations are close to Millennium MPS recently became a member of the Karen has served MPS tirelessly for over Park, around which the recent revival of International Council of Industrial and ten years as Councillor and Publications downtown Chicago has been centered. The Applied Mathematics (ICIAM), a society of Committee Chair, in addition to her most meeting will include a commemoration of societies whose main function is to organize recent role. Bill Cook did great work as the 60th anniversary of the “zero-th” ISMP, a congress every four years. I was privileged editor of Mathematical Programming Series which was held in Chicago in 1949. I hope to attend the most recent congress in Zurich B, then Series A, maintaining the high that all of you will be able to take advantage along with 3100 colleagues. The next standards of our journal over a 7-year span. of Chicago’s pleasant summer weather and congress is planned for Vancouver in 2011. Special thanks go to these three colleagues! its location as a global air hub to attend MPS members have already played key roles

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Prizes and Conferences by Katya Scheinberg The Second Mathematical Programming Out of 23 submissions three The last sentence, slightly modified, well Society International Conference on finalists were selected: expresses the committee’s feelings on the Continuous Optimization (ICCOPT II) Alexandre Belloni (Duke University), participants in this year’s Young Researcher was held at McMaster University on August Mung Chiang (Princeton University) Competition. Most of the 23 submissions 13-16, 2007. Even though only the second Eissa Nematollahi (McMaster University) were of high quality. Also, the submissions of its kind this conference was a smashing who presented their work in a special of the three finalists, Alex Belloni, Mung success. Instead of writing about it ourselves, session during the conference. The prize Chiang and Eissa Nematollahi, who we let the professional speak for us. was awarded to Alexandre Belloni for presented their papers this afternoon, his paper “Norm-induced Densities and where convincing enough for us to agree Here is a excerpt from the Testing the Boundedness of a Convex Set”. that they are up to the standard in the Hamilton Spectator: optimization community for being finalists “There is an endless number of optimization Here is how Kees Roos presented the in the competition. But our committee applications”, Terlaky says. Specialists prize at the conference banquet: also agreed unanimously that the work of develop algorithms and use computer Ludwig Wittgenstein, the most famous Belloni certainly meets the standard for networks to simulate, model and optimize logician and philosopher of language, being the winner of the competition. solutions to various problems, as well as was awarded a PhD at the university of design new products and services. “Mostly, Cambridge (UK), in 1929. As his PhD you don't see it because it's behind the thesis served the small booklet ’ ‘Tractatus scenes“, Terlaky says. “But without it, logico-philosophicus’, a work that had been Uneasy Relations by everything would be more expensive and in print already for seven years and that Michael Bartholomew- less efficient.“ It all has to do with a field of was regarded at that time by many as a research called continuous optimization, or philosophical classic. The examiners were Biggs: a Book Review more formally, mathematical programming George E. Moore and Bertrand Russell. by Andrea Lodi — finding the most efficient and effective The PhD defense was set for 18 June, means to an end. And big players like 1929, and was conducted with an air of Uneasy Relations contains poems - mainly NASA, Boeing, General Motors, which used farcical ritual. As Russell walked into the in haiku form - which play with ideas to have their own mathematics department, examination room with Moore, he smiled from computational mathematics. Non- Microsoft and Exxon Mobil rely on it to and said: ‘I have never known anything specialists may choose to murmur them improve their products or in designing new so absurd in my life’. The examination as zen-like meditations. For readers of a ones. The companies have representatives began with a chat between old friends. curious disposition, notes are provided in Hamilton this week to attend a major Then Russell, relishing the absurdity of the that may be no less informative than international conference on optimization situation, said to Moore: ‘Go on, you’ve those at the end of The Waste Land. at McMaster. The conference has also got to ask him some questions – you’re the attracted NASA representatives, PhD professor’. Then followed a short discussion Our favorite? students, professors and researchers from in which Russell advanced his view that AUXILIARIES around the world, representing Ivy League Wittgenstein was inconstant in claiming to institutions such as Princeton, Oxford, have expressed unassailable truths by means Lagrange Multipliers Stanford and MIT. About 450 specialists of meaningless propositions. He was, of These are our shadows, are attending from 36 countries, including course, unable to convince Wittgenstein, dual personalities, New Zealand, Singapore, Brazil and Chile. who brought the proceeding to an end who know what we don't — by clapping each of his examiners on the the consequences The Ivy Leagueness of Oxford, Stanford and shoulder and remarking consolingly: ‘Don’t of pushing our boundaries MIT is debatable, but everything else is true. worry, I know you’ll never understand it’. or pulling them in. From ourselves we can add that with 22 streams on numerous subjects there In his examiner’s report, Moore stated: Michael Bartholomew-Biggs has spent most was never a dull moment at this well ‘It is my personal opinion that Mr. of his working life as a mathematician at attended conference. The quality of talks Wittgenstein’s thesis is a work of a genius, the University of Hertfordshire. As the and attendance was high and discussions but, be that as it may, it is certainly well author himself says, his poetic ambitions lively. One of the highlights of the up to the standard for the Cambridge arrived as part of a mid-life crisis and conference was the Young Researchers degree of Doctor of Philosophy’. (See this, his fourth poetry chapbook, is an Competition in continuous optimization. Ray Monk, Ludwig Wittgenstein. The attempt to unite both halves of his brain. The committee consisted of Kees Roos duty of genius. Penguin Books, 1990). (chair), Arnold Neumaier, Levent Michael Bartholomew-Biggs, Uneasy Tuncel, and Akiko Yoshise. Relations, Hearing Eye London (UK), 2007. ISBN: 978-1-905082-31-5. o p t I M A mathematical programming society

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EDITOR: CO-EDITORS: founding editor: Andrea Lodi Alberto Caprara Donald W. Hearn DEIS University of Bologna, DEIS University of Bologna, Viale Risorgimento 2, Viale Risorgimento 2, published by the I - 40136 Bologna, Italy I - 40136 Bologna, Italy mathematical programming society & e-mail: [email protected] e-mail: [email protected] University of Florida

Katya Scheinberg Journal contents are subject to IBM T.J. Watson Research Center change by the publisher. PO Box 218 Yorktown Heights, NY 10598, USA [email protected]