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Full-Text Articles in Mathematics
Relative Pareto Minimizers To Multiobjective Problems: Existence And Optimality Conditions, Truong Q. Bao, Boris S. Mordukhovich
Relative Pareto Minimizers To Multiobjective Problems: Existence And Optimality Conditions, Truong Q. Bao, Boris S. Mordukhovich
Mathematics Research Reports
In this paper we introduce and study enhanced notions of relative Pareto minimizers to constrained multiobjective problems that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical notions of Pareto and weak Pareto efficiency/minimality. Using advanced tools of variational analysis and generalized differentiation, we establish the existence of relative Pareto minimizers to general multiobjective problems under a refined version of the subdifferential Palais-Smale condition for set-valued mappings with values in partially ordered spaces and then derive necessary optimality conditions for these minimizers (as well as for conventional efficient and weak efficient …
Necessary Conditions For Super Minimizers In Constrained Multiobjective Optimization, Truong Q. Bao, Boris S. Mordukhovich
Necessary Conditions For Super Minimizers In Constrained Multiobjective Optimization, Truong Q. Bao, Boris S. Mordukhovich
Mathematics Research Reports
This paper concerns the study of the so-called super minimizers related to the concept of super efficiency in constrained problems of multiobjective optimization, where cost mappings are generally set-valued. We derive necessary conditions for super minimizers on the base of advanced tools of variational analysis and generalized differentiation that are new in both finite-dimensional and infinite-dimensional settings for problems with single-valued and set-valued objectives.
Suboptimality Conditions For Mathematical Programs With Equilibrium Constraints, Truong Q. Bao, Panjak Gupta, Boris S. Mordukhovich
Suboptimality Conditions For Mathematical Programs With Equilibrium Constraints, Truong Q. Bao, Panjak Gupta, Boris S. Mordukhovich
Mathematics Research Reports
In this paper we study mathematical programs with equilibrium constraints (MPECs) described by generalized equations in the extended 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 arise, in particular, from certain optimization-related problems governed by variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish new weak and strong suboptimality conditions for the general MPEC problems under consideration in finite-dimensional and infinite-dimensional spaces that do not assume the existence of optimal solutions. This issue is particularly important for infinite-dimensional optimization problems, where the existence of optimal …
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.