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One-step optimization method for equilibrium problems

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Abstract

The paper introduces an one-step optimization method for solving a monotone equilibrium problem including a Lipschitz-type condition in a Hilbert space. The method uses variable stepsizes and is constructed by the proximal-like mapping associated with the cost bifunction and incorporated with regularization terms. Comparing with the extragradient-like methods, our new method has an elegant and simple structure with a cheap computation over each iteration. By an appropriate choice of stepsizes and regularization parameters, we establish the strong convergence of the iterative sequence generated by the method to a solution of the considered equilibrium problem. We also show the numerical behavior of our new method and illustrate the computational effectiveness of it over other methods via experiments.

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Acknowledgements

The authors sincerely thank the Editor and anonymous reviewers for their constructive comments which helped to improve the quality and presentation of this paper.

Funding

The research of two first authors is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2020.06.

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Authors and Affiliations

  1. TIMAS - Thang Long University, Hanoi, Vietnam

    Dang Van Hieu

  2. Institute of Mathematics - VAST, Hanoi, Vietnam

    Le Dung Muu

  3. Department of Basic Sciences, College of Air Force, Nha Trang, Vietnam

    Pham Kim Quy

Authors
  1. Dang Van Hieu
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  2. Le Dung Muu
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  3. Pham Kim Quy
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Correspondence to Dang Van Hieu.

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The authors declare no competing interests. All authors have contributed equally.

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Communicated by: Russell Luke

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Van Hieu, D., Muu, L.D. & Quy, P.K. One-step optimization method for equilibrium problems. Adv Comput Math 48, 29 (2022). https://doi.org/10.1007/s10444-022-09953-3

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  • DOI: https://doi.org/10.1007/s10444-022-09953-3

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