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Alternated inertial subgradient extragradient method for equilibrium problems

Author

Listed:
  • Yekini Shehu

    (Zhejiang Normal University)

  • Qiao-Li Dong

    (Civil Aviation University of China)

  • Lulu Liu

    (Civil Aviation University of China)

  • Jen-Chih Yao

    (China Medical University)

Abstract

The focus of this paper is to obtain weak and linear convergence analysis of the subgradient extragradient method with alternated inertial step for solving equilibrium problems in real Hilbert spaces. The proposed method uses self-adaptive step sizes. Weak convergence is established without Lipschitz constant of the bifunction as an input parameter. Linear convergence is obtained without the modulus of strong pseudomonotonicity and Lipschitz constant as input parameters. We report some priori and posteriori error estimates and some numerical experiments to illustrate the behavior of our proposed method with related methods.

Suggested Citation

  • Yekini Shehu & Qiao-Li Dong & Lulu Liu & Jen-Chih Yao, 2023. "Alternated inertial subgradient extragradient method for equilibrium problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 1-30, April.
    • Handle: RePEc:spr:topjnl:v:31:y:2023:i:1:d:10.1007_s11750-021-00620-2
    DOI: 10.1007/s11750-021-00620-2
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    References listed on IDEAS

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    1. Dang Hieu, 2018. "An inertial-like proximal algorithm for equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 399-415, December.
    2. J. Preininger & P. T. Vuong, 2018. "On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions," Computational Optimization and Applications, Springer, vol. 70(1), pages 221-238, May.
    3. Thi Thu Van Nguyen & Jean Jacques Strodiot & Van Hien Nguyen, 2014. "Hybrid Methods for Solving Simultaneously an Equilibrium Problem and Countably Many Fixed Point Problems in a Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 809-831, March.
    4. Franck Iutzeler & Jérôme Malick, 2018. "On the Proximal Gradient Algorithm with Alternated Inertia," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 688-710, March.
    5. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
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