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Levitin–Polyak well-posedness of vector equilibrium problems

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  • S. Li
  • M. Li

Abstract

In this paper, two types of Levitin–Polyak well-posedness of vector equilibrium problems with variable domination structures are investigated. Criteria and characterizations for two types of Levitin–Polyak well-posedness of vector equilibrium problems are shown. Moreover, by virtue of a gap function for vector equilibrium problems, the equivalent relations between the Levitin–Polyak well-posedness for an optimization problem and the Levitin–Polyak well-posedness for a vector equilibrium problem are obtained. Copyright Springer-Verlag 2009

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  • S. Li & M. Li, 2009. "Levitin–Polyak well-posedness of vector equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 125-140, March.
    • Handle: RePEc:spr:mathme:v:69:y:2009:i:1:p:125-140
    DOI: 10.1007/s00186-008-0214-0
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    References listed on IDEAS

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    1. G. Y. Chen & X. Q. Yang, 2002. "Characterizations of Variable Domination Structures via Nonlinear Scalarization," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 97-110, January.
    2. G. Y. Chen & C. J. Goh & X. Q. Yang, 1999. "Vector network equilibrium problems and nonlinear scalarization methods," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(2), pages 239-253, April.
    3. S. Li & K. Teo & X. Yang, 2005. "Generalized vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 385-397, July.
    4. M. Bianchi & N. Hadjisavvas & S. Schaible, 1997. "Vector Equilibrium Problems with Generalized Monotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 527-542, March.
    5. S. J. Li & Hong Yan & G. Y. Chen, 2003. "Differential and sensitivity properties of gap functions for vector variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 377-391, August.
    6. D.E. Ward & G.M. Lee, 2002. "On Relations Between Vector Optimization Problems and Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 583-596, June.
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    Cited by:

    1. 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.
    2. 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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