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Levitin–Polyak well-posedness by perturbations for systems of set-valued vector quasi-equilibrium problems

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  • Jia-Wei Chen
  • Zhongping Wan
  • Yeol Cho

Abstract

This paper is devoted to the Levitin–Polyak well-posedness by perturbations for a class of general systems of set-valued vector quasi-equilibrium problems (SSVQEP) in Hausdorff topological vector spaces. Existence of solution for the system of set-valued vector quasi-equilibrium problem with respect to a parameter (PSSVQEP) and its dual problem are established. Some sufficient and necessary conditions for the Levitin–Polyak well-posedness by perturbations are derived by the method of continuous selection. We also explore the relationships among these Levitin–Polyak well-posedness by perturbations, the existence and uniqueness of solution to (SSVQEP). By virtue of the nonlinear scalarization technique, a parametric gap function g for (PSSVQEP) is introduced, which is distinct from that of Peng (J Glob Optim 52:779–795, 2012 ). The continuity of the parametric gap function g is proved. Finally, the relations between these Levitin–Polyak well-posedness by perturbations of (SSVQEP) and that of a corresponding minimization problem with functional constraints are also established under quite mild assumptions. Copyright Springer-Verlag Berlin Heidelberg 2013

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  • Jia-Wei Chen & Zhongping Wan & Yeol Cho, 2013. "Levitin–Polyak well-posedness by perturbations for systems of set-valued vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 33-64, February.
    • Handle: RePEc:spr:mathme:v:77:y:2013:i:1:p:33-64
    DOI: 10.1007/s00186-012-0414-5
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    References listed on IDEAS

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    Cited by:

    1. Savin Treanţă, 2021. "On Well-Posedness of Some Constrained Variational Problems," Mathematics, MDPI, vol. 9(19), pages 1-12, October.
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    3. J. W. Chen & Y. J. Cho & S. A. Khan & Z. Wan & C. F. Wen, 2015. "The Levitin-Polyak well-posedness by perturbations for systems of general variational inclusion and disclusion problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(6), pages 901-920, December.

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