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Optimality Condition for Local Efficient Solutions of Vector Equilibrium Problems via Convexificators and Applications

Journal of Optimization Theory and Applications volume 171, pages 643–665 (2016)Cite this article

Abstract

Fritz John and Karush–Kuhn–Tucker necessary conditions for local efficient solutions of constrained vector equilibrium problems in Banach spaces in which those solutions are regular in the sense of Ioffe via convexificators are established. Under suitable assumptions on generalized convexity, sufficient conditions are derived. Some applications to constrained vector variational inequalities and constrained vector optimization problems are also given.

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Acknowledgments

The author is grateful to the referees for their valuable comments and suggestions which improve the paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2014.61.

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Authors and Affiliations

  1. Institute of Mathematics, Vietnam Academy of Science and Technology, Thang Long University, Hanoi, Vietnam

    Do Van Luu

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  1. Do Van Luu
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Correspondence to Do Van Luu.

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Van Luu, D. Optimality Condition for Local Efficient Solutions of Vector Equilibrium Problems via Convexificators and Applications. J Optim Theory Appl 171, 643–665 (2016). https://doi.org/10.1007/s10957-015-0815-8

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  • DOI: https://doi.org/10.1007/s10957-015-0815-8

Keywords

  • Vector equilibrium problems
  • Vector variational inequalities
  • Vector optimization problems
  • Regular points in the sense of Ioffe
  • Fritz John and Karush–Kuhn–Tucker optimality conditions
  • Convexificators

Mathematics Subject Classification

  • 90C46
  • 91B50
  • 49J52