Necessary Conditions in Multiobjective Optimization with Equilibrium Constraints
We study multiobjective optimization problems with equilibrium constraints (MOPECs) described by parametric generalized equations in the form
where both mappings G and Q are set-valued. Such models arise particularly 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 by 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.
KeywordsVariational analysis Nonsmooth and multiobjective optimization Variational inequalities Equilibrium constraints Bilevel programming Necessary optimality conditions Generalized differentiation
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