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Levitin–Polyak well-posedness of vector equilibrium problems

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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.

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Authors and Affiliations

  1. College of Mathematics and Sciences, Chongqing University, Chongqing, 400044, China

    S. J. Li & M. H. Li

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  1. S. J. Li
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  2. M. H. Li
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Correspondence to S. J. Li.

Additional information

This research was partially supported by the National Natural Science Foundation of China (Grant number: 60574073) and Natural Science Foundation Project of CQ CSTC (Grant number: 2007BB6117).

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Li, S.J., Li, M.H. Levitin–Polyak well-posedness of vector equilibrium problems. Math Meth Oper Res 69, 125–140 (2009). https://doi.org/10.1007/s00186-008-0214-0

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  • DOI: https://doi.org/10.1007/s00186-008-0214-0

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