Necessary conditions for multiobjective optimization with equilibrium constraints
J. Optim. Theory Appl.
Mathematics and Computer Science
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.
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.