Article Title

Necessary conditions for multiobjective optimization with equilibrium constraints

Journal Title/Source

J. Optim. Theory Appl.

Publication Date

2007

Volume

135

Page Numbers

179-203

Document Type

Journal Article

Department

Mathematics and Computer Science

Abstract

In this paper we study multiobjective optimization problems with equilibrium constraints (MOPECs) described by parametric generalized equations in the form $0 \in G(x,y)+Q(x,y)$, where both mappings $G$ and $Q$ are set-valued. Such models particularly arise from certain optimization-related problems governed by variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish verifiable necessary conditions for the general problems under consideration and for their important specifications using modern tools of variational analysis and generalized differentiation. The application of the obtained necessary optimality conditions is illustrated by a numerical example from bilevel programming with convex while nondifferentiable data.