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Full-Text Articles in Applied Mathematics
Existence Of Minimizers And Necessary Conditions In Set-Valued Optimization With Equilibrium Constraints, Truong Q. Bao, Boris S. Mordukhovich
Existence Of Minimizers And Necessary Conditions In Set-Valued Optimization With Equilibrium Constraints, Truong Q. Bao, Boris S. Mordukhovich
Mathematics Research Reports
In this paper we study set-valued optimization problems with equilibrium constraints (SOPEOs) described by parametric generalized equations in the form 0 is an element of the set 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 PalaisSmale type and then derive necessary conditions for optimality in the models under consideration by using advanced tools of variational analysis and generalized differentiation.
Multiobjective Optimization Problems With Equilibrium Constraints, Boris S. Mordukhovich
Multiobjective Optimization Problems With Equilibrium Constraints, Boris S. Mordukhovich
Mathematics Research Reports
The paper is devoted to new applications of advanced tools of modern variational analysis and generalized differentiation to the study of broad classes of multiobjective optimization problems subject to equilibrium constraints in both finite-dimensional and infinite-dimensional settings. Performance criteria in multiobjectivejvector optimization are defined by general preference relationships satisfying natural requirements, while equilibrium constraints are described by parameterized generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically nonsmooth and are handled in this paper via appropriate normal/coderivativejsubdifferential constructions that exhibit full calculi. Most of the results obtained are new even in finite dimensions, while the case of …
Necessary Conditions In Multiobjective Optimization With Equilibrium Constraints, Truong Q. Bao, Panjak Gupta, Boris S. Mordukhovich
Necessary Conditions In Multiobjective Optimization With Equilibrium Constraints, Truong Q. Bao, Panjak Gupta, Boris S. Mordukhovich
Mathematics Research Reports
In this paper we study multiobjective optimization problems with equilibrium constraints (MOECs) described by generalized equations in the form 0 is an element of the set 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 …
Optimization And Equilibrium Problems With Equilibrium Constraints, Boris S. Mordukhovich
Optimization And Equilibrium Problems With Equilibrium Constraints, Boris S. Mordukhovich
Mathematics Research Reports
The paper concerns optimization and equilibrium problems with the so-called equilibrium constraints (MPEC and EPEC), which frequently appear in applications to operations research. These classes of problems can be naturally unified in the framework of multiobjective optimization with constraints governed by parametric variational systems (generalized equations, variational inequalities, complementarity problems, etc.). We focus on necessary conditions for optimal solutions to MPECs and EPECs under general assumptions in finite-dimensional spaces. Since such problems are intrinsically nonsmooth, we use advanced tools of generalized differentiation to study optimal solutions by methods of modern variational analysis. The general results obtained are concretized for special …