In this paper we study set-valued optimization problems with equilibrium constraints (SOPEOs) described by parametric generalized equations in the form 0 is an element of the set G(x) + Q(x) where both G and Q are set-valued mappings between infinite-dimensional spaces. Such models particularly arise from certain optimization-related problems governed by set-valued variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish general results on the existence of optimal solutions under appropriate assumptions of the PalaisSmale type and then derive necessary conditions for optimality in the models under consideration by using advanced tools of variational analysis and generalized differentiation.
Number in Series
Applied Mathematics | Mathematics
AMS Subject Classification
49J53, 49J52, 90C29, 90A14, 90C33
Bao, Truong Q. and Mordukhovich, Boris S., "Existence of Minimizers and Necessary Conditions in Set-Valued Optimization with Equilibrium Constraints" (2007). Mathematics Research Reports. 50.