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.
Recommended Citation
Bao, T. Q.; Gupta, P.; Mordukhovich, B. S. Necessary conditions in multiobjective optimization with equilibrium constraints. J. Optim. Theory Appl. 135 (2007), no. 2, 179–203.