Journal Article10.1007/S10898-006-9012-5
Strong Vector Equilibrium Problems
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TL;DR: In this article, the existence of strong vector equilibrium problems is studied by using the separation theorem for convex sets, and the arc-wise connectedness and the closedness of the strong solution set are discussed.
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Abstract: In this paper, the existence of the solution for strong vector equilibrium problems is studied by using the separation theorem for convex sets. The arc-wise connectedness and the closedness of the strong solution set for vector equilibrium problems are discussed; and a necessary and sufficient condition for the strong solution is obtained.
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Citations
Optimality conditions for vector equilibrium problems
TL;DR: In this paper, the necessary and sufficient conditions for weakly efficient, Henig efficient, globally efficient, and superefficient solution to the vector equilibrium problems with constraints are presented. But the necessary conditions for corresponding solution to vector variational inequalities and vector optimization problems are not discussed.
64
Connectedness of the Set of Efficient Solutions for Generalized Systems
X. H. Gong,Jen-Chih Yao +1 more
TL;DR: The set of positive proper efficient solutions is dense in the set of efficient solutions to the generalized system with monotone bifunctions in real locally convex Hausdorff topological vector spaces.
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Existence and stability of solutions for generalized strong vector quasi-equilibrium problem
TL;DR: An existence theorem of solutions for the generalized strong vector quasi-equilibrium problem is established by using Kakutani-Fan-Glicksberg fixed point theorem and the closedness of the strong solution set is discussed.
53
Optimality conditions for various efficient solutions involving coderivatives: From set-valued optimization problems to set-valued equilibrium problems
TL;DR: In this paper, a new approach to the study of various ecient solutions of a set-valued equilibrium problem (for short, SEP) is presented through theStudy of corresponding solutions ofA set- valued optimization problem with a geometric constraint ( for short, SOP).
35
Existence and stability of solutions for a class of generalized vector equilibrium problems
Yu Han,Nan-Jing Huang +1 more
TL;DR: In this article, two existence theorems concerning the strong efficient solutions and the weakly efficient solutions of generalized vector equilibrium problems are derived by using the Fan-KKM Theorem and an existence theorem for the efficient solution of GVE problems is established by using scalarization method.
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References
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TL;DR: In this paper, the authors give necessary and sufficient conditions for extending a family of point-to-set maps to a point-set map which can be applied to abstract algorithms with global convergence.
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TL;DR: In this article, the vector quasivariational inequalities and vector variational inequalities for multifunctions with vector values were studied and the existence theorems of solutions for these inequalities were proved.
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Existence of solutions for a generalized vector quasivariational inequality
G. Y. Chen,S. J. Li +1 more
TL;DR: In this article, Fan's section theorem for set-valued mappings is extended to an equilibrium problem of a network with vector-valued cost functions and an existence theorem for its solutions is established; it is based on a kind of minimax inequality.
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