Multiobjective optimization problems with equilibrium constraints

The paper is devoted to new applications of advanced tools of modern variational analysis and generalized differentiation to the study of broad classes of multiobjective optimization problems subject to equilibrium constraints in both finite-dimensional and infinite-dimensional settings. Performance criteria in multiobjective/vector optimization are defined by general preference relationships satisfying natural requirements, while equilibrium constraints are described by parameterized generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically nonsmooth and are handled in this paper via appropriate normal/coderivative/subdifferential constructions that exhibit full calculi. Most of the results obtained are new even in finite dimensions, while the case of infinite-dimensional spaces is significantly more involved requiring in addition certain “sequential normal compactness” properties of sets and mappings that are preserved under a broad spectrum of operations.