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On penalty method for equilibrium problems in lexicographic order

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Abstract

In this paper, we consider lexicographic vector equilibrium problems. We propose a penalty function method for solving such problems. We show that every penalty trajectory of the penalized lexicographic equilibrium problem tends to the solution of the original problem. Using the regularized gap function to obtain an error bound result for such penalized problems is given.

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Acknowledgements

The authors wish to thank the anonymous referees for the careful reviews and valuable comments that helped us significantly improve the presentation of the paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2017.18.

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Authors and Affiliations

  1. Department of Mathematics, Teacher College, Cantho University, Cantho, Vietnam

    L. Q. Anh

  2. Department of Mathematics, Cantho Technical and Economic College, Cantho, Vietnam

    T. Q. Duy

  3. Department of Mathematics, University of Science, Vietnam National University Ho Chi Minh City, Ho Chi Minh City, Vietnam

    T. Q. Duy

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  1. L. Q. Anh
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  2. T. Q. Duy
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Correspondence to T. Q. Duy.

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Anh, L.Q., Duy, T.Q. On penalty method for equilibrium problems in lexicographic order. Positivity 22, 39–57 (2018). https://doi.org/10.1007/s11117-017-0496-7

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  • DOI: https://doi.org/10.1007/s11117-017-0496-7

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