Existence of minimizers and necessary conditions in set-valued optimization with equilibrium constraints |
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Authors: | Truong Q Bao Boris S Mordukhovich |
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Institution: | (1) Department of Mathematics, Wayne State University, Detroit, MI 48202, USA |
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Abstract: | In this paper we study set-valued optimization problems with equilibrium constraints (SOPECs) described by parametric generalized
equations in the form 0 ∈ 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.
Dedicated to Jiří V. Outrata on the occasion of his 60th birthday.
This research was partly supported by the National Science Foundation under grants DMS-0304989 and DMS-0603846 and by the
Australian Research Council under grant DP-0451168. |
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Keywords: | variational analysis nonsmooth and set-valued optimization equilibrium constraints existence of optimal solutions necessary optimality conditions generalized differentiation |
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