The paper is devoted to applications of modern variational f).nalysis to the study of constrained optimization and equilibrium problems in infinite-dimensional spaces. We pay a particular attention to the remarkable classes of optimization and equilibrium problems identified as MPECs (mathematical programs with equilibrium constraints) and EPECs (equilibrium problems with equilibrium constraints) treated from the viewpoint of multiobjective optimization. Their underlying feature is that the major constraints are governed by parametric generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically nonsmooth and can be handled by using an appropriate machinery of generalized differentiation exhibiting a rich/full calculus. The case of infinite-dimensional spaces is significantly more involved in comparison with finite dimensions, requiring in addition a certain sufficient amount of compactness and an efficient calculus of the corresponding "sequential normal compactness" (SNC) properties.
Number in Series
Applied Mathematics | Mathematics
AMS Subject Classification
90C29, 90C30, 49J52, 49J53, 49K27
Mordukhovich, Boris S., "Optimization and Equilibrium Problems with Equilibrium Constraints in Infinite-Dimensional Spaces" (2006). Mathematics Research Reports. 33.