Strongly convergent algorithms by using new adaptive regularization parameter for equilibrium problems

Dang Van Hieu, Jean Jacques Strodiot, Le Dung Muu

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Two new algorithms are proposed in this paper for solving an equilibrium problem whose associated bifunction is monotone and satisfies a Lipschitz-type condition in a Hilbert space. In the first algorithm, it is assumed that the value of the Lipschitz constant of the bifunction is known while in the second one the prior knowledge of this constant is not explicitly requested. The proposed algorithms are constructed around the proximal-like mapping and the regularized method and use some new variable stepsize rules. Strong convergence theorems are established under some mild conditions imposed on bifunction and control parameters. Finally several numerical results are provided to illustrate the behavior of the new algorithms and to compare them to well-known algorithms.

    Original languageEnglish
    Article number112844
    Journal Journal of Computational and Applied Mathematics
    Volume376
    DOIs
    Publication statusPublished - 1 Oct 2020

    Keywords

    • Equilibrium problem
    • Extragradient method
    • Lipschitz-type bifunction
    • Regularized method

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