Iterative Methods for Solving Optimization Problems
ITERATIVE METHODS FOR SOLVING OPTIMIZATION PROBLEMS Shoham Sabach ITERATIVE METHODS FOR SOLVING OPTIMIZATION PROBLEMS Research Thesis In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Shoham Sabach Submitted to the Senate of the Technion - Israel Institute of Technology Iyar 5772 Haifa May 2012 The research thesis was written under the supervision of Prof. Simeon Reich in the Department of Mathematics Publications: piq Reich, S. and Sabach, S.: Three strong convergence theorems for iterative methods for solving equi- librium problems in reflexive Banach spaces, Optimization Theory and Related Topics, Contemporary Mathematics, vol. 568, Amer. Math. Soc., Providence, RI, 2012, 225{240. piiq Mart´ın-M´arquez,V., Reich, S. and Sabach, S.: Iterative methods for approximating fixed points of Bregman nonexpansive operators, Discrete and Continuous Dynamical Systems, accepted for publi- cation. Impact Factor: 0.986. piiiq Sabach, S.: Products of finitely many resolvents of maximal monotone mappings in reflexive Banach spaces, SIAM Journal on Optimization 21 (2011), 1289{1308. Impact Factor: 2.091. pivq Kassay, G., Reich, S. and Sabach, S.: Iterative methods for solving systems of variational inequalities in reflexive Banach spaces, SIAM J. Optim. 21 (2011), 1319{1344. Impact Factor: 2.091. pvq Censor, Y., Gibali, A., Reich S. and Sabach, S.: The common variational inequality point problem, Set-Valued and Variational Analysis 20 (2012), 229{247. Impact Factor: 0.333. pviq Borwein, J. M., Reich, S. and Sabach, S.: Characterization of Bregman firmly nonexpansive operators using a new type of monotonicity, J. Nonlinear Convex Anal. 12 (2011), 161{183. Impact Factor: 0.738. pviiq Reich, S.
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