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Reflected Iterative Method for Non-Monotone Equilibrium Problems with Applications to Nash-Cournot Equilibrium Models

Author

Listed:
  • Yekini Shehu

    (Zhejiang Normal University)

  • Lulu Liu

    (Civil Aviation University of China)

  • Xiaolong Qin

    (Zhejiang Normal University)

  • Qiao-Li Dong

    (Civil Aviation University of China)

Abstract

In this paper, we introduce a numerical iterative algorithm with a reflected step to solve the equilibrium problem, which involves non-monotone bifunctions, in real Hilbert spaces. We give weak convergence analysis when the bifunctions are convex and jointly weakly continuous alongside the associated Minty equilibrium problem with a solution. The assumptions in this paper are weaker than the pseudo-monotonicity Lipschitz-type continuity assumptions used recently on equilibrium problems in the literature. Numerical results on Nash-Cournot equilibrium models show that our algorithm is competitive and efficient.

Suggested Citation

  • Yekini Shehu & Lulu Liu & Xiaolong Qin & Qiao-Li Dong, 2022. "Reflected Iterative Method for Non-Monotone Equilibrium Problems with Applications to Nash-Cournot Equilibrium Models," Networks and Spatial Economics, Springer, vol. 22(1), pages 153-180, March.
    • Handle: RePEc:kap:netspa:v:22:y:2022:i:1:d:10.1007_s11067-022-09562-z
    DOI: 10.1007/s11067-022-09562-z
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    References listed on IDEAS

    as
    1. Jean Strodiot & Thi Nguyen & Van Nguyen, 2013. "A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems," Journal of Global Optimization, Springer, vol. 56(2), pages 373-397, June.
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