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Full-Text Articles in Physical Sciences and 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.
Variational Principles For Set-Valued Mappings With Applications To Multiobjective Optimization, Truong Q. Bao, Boris S. Mordukhovich
Variational Principles For Set-Valued Mappings With Applications To Multiobjective Optimization, Truong Q. Bao, Boris S. Mordukhovich
Mathematics Research Reports
This paper primarily concerns the study of general classes of constrained multiobjective optimization problems (including those described via set-valued and vector-valued cost mappings) from the viewpoint of modern variational analysis and generalized differentiation. To proceed, we first establish two variational principles for set-valued mappings, which~being certainly of independent interest are mainly motivated by applications to multiobjective optimization problems considered in this paper. The first variational principle is a set-valued counterpart of the seminal derivative-free Ekeland variational principle, while the second one is a set-valued extension of the subdifferential principle by Mordukhovich and Wang formulated via an appropriate subdifferential notion for …