Session: Algorithms for Nonconvex Problems
Chair: Yulin Peng
Cluster:
Talk 1: NEW ALGORITHMS FOR HARD OPTIMIZATION problems PROBLEMS.
Speaker: Aharonl Ben-Tal
Abstract: NEW ALGORITHMS FOR HARD (NONCONVEX) OPTIMIZATION PROBLEMS. The problems addressed in this talk are: (1) Max of convex function (2) Max of max of convex function (3) Max of Difference of convex functions. Almost all existing algorithms for such problems suffer from might be called “the curse of obtaining a good starting point”. In our algorithms a starting point is computed by employing only tractable methods for convex problems. The core algorithm on which the algorithms for problems (2) and (3) are based, is the COMAX algorithm developed for problem (1), See Ben-Tal, A. and Roos E., "An Algorithm for Maximizing a Convex Function Based on its Minimizer". INFORMS Journal on Computing Volume: 34, Number: 6 (November-December 2022): 3200-
Talk 2: Quasi-Difference-Convexity: Modernization of Quasi-differentiable Optimization
Speaker: Yulin Peng
Abstract: We begin by formally defining quasi-difference-convex functions in several variables and illustrating their broad modeling breadth. We then consider the minimization of a class of composite quasi-difference-convex functions using descent methods combined with line search strategies. We establish subsequential convergence of the proposed approach, and under additional assumptions, we further prove full sequential convergence.
Talk 3: Conditional Infimum, Hidden Convexity and the S-Procedure
Speaker: Michel De Lara
