Optimization and equilibrium problems with equilibrium constraints in infinite-dimensional spaces

Abstract

The article is devoted to applications of modern variational analysis 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 mathematical programs with equilibrium constraints (MPECs) and equilibrium problems with equilibrium constraints (EPECs) 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 non-smooth 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.