Document Type

Technical Report


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


Dedicated to Jiri Outrata in honor of his 60th birthday. This research was partly supported by the National Science Foundation under grants DMS-0304989 and DMS-0603846 and by the Australian Research Council under grant DP-0451168.