Existence of minimizers and necessary conditions in set-valued optimization with equilibrium constraints

Truong Q. Bao; Boris S. Mordukhovich

Applications of Mathematics (2007)

  • Volume: 52, Issue: 6, page 453-472
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Bao, Truong Q., and Mordukhovich, Boris S.. "Existence of minimizers and necessary conditions in set-valued optimization with equilibrium constraints." Applications of Mathematics 52.6 (2007): 453-472. <http://eudml.org/doc/33303>.

@article{Bao2007,
abstract = {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.},
author = {Bao, Truong Q., Mordukhovich, Boris S.},
journal = {Applications of Mathematics},
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},
language = {eng},
number = {6},
pages = {453-472},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of minimizers and necessary conditions in set-valued optimization with equilibrium constraints},
url = {http://eudml.org/doc/33303},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Bao, Truong Q.
AU - Mordukhovich, Boris S.
TI - Existence of minimizers and necessary conditions in set-valued optimization with equilibrium constraints
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 6
SP - 453
EP - 472
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/33303
ER -

References

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