Applications of Mathematics

, Volume 52, Issue 6, pp 453–472 | Cite as

Existence of minimizers and necessary conditions in set-valued optimization with equilibrium constraints

Abstract

In this paper we study set-valued optimization problems with equilibrium constraints (SOPECs) described by parametric generalized equations in the form 0 ∈ 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 Palais-Smale type and then derive necessary conditions for optimality in the models under consideration by using advanced tools of variational analysis and generalized differentiation.

Keywords

variational analysis nonsmooth and set-valued optimization equilibrium constraints existence of optimal solutions necessary optimality conditions generalized differentiation 

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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2007

Authors and Affiliations

  1. 1.Department of MathematicsWayne State UniversityDetroitUSA

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