Article
MSC:
49J52,
49J53,
90C29,
90C30,
90C33 | MR 2357575 | Zbl 1164.49306 | DOI: 10.1007/s10492-007-0027-0
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Keywords:
variational analysis; nonsmooth and set-valued optimization; equilibrium constraints; existence of optimal solutions; necessary optimality conditions; generalized differentiation
variational analysis; nonsmooth and set-valued optimization; equilibrium constraints; existence of optimal solutions; necessary optimality conditions; generalized differentiation
Summary:
In this paper we study set-valued optimization problems with equilibrium constraints (SOPECs) described by parametric generalized equations in the form \[ 0\in G(x)+Q(x), \] 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.
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