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DC auxiliary principle methods for solving lexicographic equilibrium problems

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Abstract

In this paper, we present DC (difference of convex functions) auxiliary principle methods for solving lexicographic equilibrium problems. Under the strongly monotone and Lipchitz-type assumptions of the cost bifunction, we study the convergence of the sequence generated by the proposed algorithms to a unique solution of the considered lexicographic equilibrium problem. Moreover, we also study the asymptotic behavior of the algorithm for solving the considered problem under the presence of computational errors. Finally, we give some numerical experiments to illustrate the behaviour of the proposed algorithms and provide their comparison with some known algorithms.

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Acknowledgements

Authors are very much grateful to the handling Editor and two anonymous referees for their helpful and constructive comments that helped us very much to improve the paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2019.303.

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Authors and Affiliations

  1. Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam

    Pham Ngoc Anh

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India

    Qamrul Hasan Ansari

  3. Department of Mathematics, Haiphong University, Haiphong, Vietnam

    Ho Phi Tu

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  1. Pham Ngoc Anh
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  3. Ho Phi Tu
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Correspondence to Qamrul Hasan Ansari.

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Anh, P.N., Ansari, Q.H. & Tu, H.P. DC auxiliary principle methods for solving lexicographic equilibrium problems. J Glob Optim 85, 129–153 (2023). https://doi.org/10.1007/s10898-022-01200-9

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