Optimality conditions for various efficient solutions involving coderivatives: From set-valued optimization problems to set-valued equilibrium problems

We present a new approach to the study of a set-valued equilibrium problem (for short, SEP) through the study of a set-valued optimization problem with a geometric constraint (for short, SOP) based on an equivalence between solutions of these problems. As illustrations, we adapt to SEP enhanced noti...

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Vydané v:	Nonlinear analysis Ročník 75; číslo 3; s. 1305 - 1323
Hlavný autor:	Ha, Truong Xuan Duc
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier Ltd 01.02.2012 Elsevier
Predmet:	Approximation Banach space Calculus of variations and optimal control Coderivative Exact sciences and technology Geometric constraints Global analysis, analysis on manifolds Inequalities Mathematical analysis Mathematics Necessary optimality conditions Normal cone Optimization Pareto efficient solutions Pareto optimality Properly efficient solutions Quasi weakly efficient solutions Relative efficient solutions Sciences and techniques of general use Set-valued equilibrium problem Set-valued optimization problem Strongly efficient solutions Sufficient optimality conditions Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Vector equilibrium problem Vector variational inequality Vectors (mathematics) Weakly efficient solutions Quasi weakly efficient solutions Sufficient optimality conditions Necessary optimality conditions Normal cone Pareto efficient solutions Coderivative Set-valued equilibrium problem Relative efficient solutions 90C29 Weakly efficient solutions 49J53 Properly efficient solutions Strongly efficient solutions 90C33 Vector equilibrium problem 49K27 Vector variational inequality Set-valued optimization problem Optimization method Variational inequality Mathematical model Nonlinear analysis Necessary condition Sufficient condition Optimality condition
ISSN:	0362-546X, 1873-5215
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