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DC auxiliary principle methods for solving lexicographic equilibrium problems

Author

Listed:
  • Pham Ngoc Anh

    (Posts and Telecommunications Institute of Technology)

  • Qamrul Hasan Ansari

    (Aligarh Muslim University)

  • Ho Phi Tu

    (Haiphong University)

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.

Suggested Citation

  • Pham Ngoc Anh & Qamrul Hasan Ansari & Ho Phi Tu, 2023. "DC auxiliary principle methods for solving lexicographic equilibrium problems," Journal of Global Optimization, Springer, vol. 85(1), pages 129-153, January.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:1:d:10.1007_s10898-022-01200-9
    DOI: 10.1007/s10898-022-01200-9
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    References listed on IDEAS

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    1. D. Han, 2007. "Inexact Operator Splitting Methods with Selfadaptive Strategy for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 227-243, February.
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    3. Lu-Chuan Zeng & Jen-Chih Yao, 2005. "Convergence analysis of a modified inexact implicit method for general mixed monotone variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 211-224, November.
    4. P. Anh & T. Hai & P. Tuan, 2016. "On ergodic algorithms for equilibrium problems," Journal of Global Optimization, Springer, vol. 64(1), pages 179-195, January.
    5. M. Seetharama Gowda & Jong-Shi Pang, 1994. "Stability Analysis of Variational Inequalities and Nonlinear Complementarity Problems, via the Mixed Linear Complementarity Problem and Degree Theory," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 831-879, November.
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