#### Title

Optimization and Equilibrium Problems with Equilibrium Constraints in Infinite-Dimensional Spaces

#### Document Type

Technical Report

#### Abstract

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

2006.03

#### Disciplines

Applied Mathematics | Mathematics

#### AMS Subject Classification

90C29, 90C30, 49J52, 49J53, 49K27

#### Recommended Citation

Mordukhovich, Boris S., "Optimization and Equilibrium Problems with Equilibrium Constraints in Infinite-Dimensional Spaces" (2006). *Mathematics Research Reports*. 33.

https://digitalcommons.wayne.edu/math_reports/33

## Comments

Research was .partially supported by the National Science Foundation under grant DMS-0304989 and by the Australian Research Council under grant DP-0451168.