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One-Step iterative method for bilevel equilibrium problem in Hilbert space

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Abstract

The purpose of this paper is to introduce a simple iterative method for finding a solution of an equilibrium problem whose constraint is the solution set of another monotone equilibrium problem in a Hilbert space. Unlike the multi-step methods, the new method only requires to find one value of the proximal mapping associated with cost bifunctions at the current approximation over each iterative step. The strong convergence of the iterative sequence generated by the method is established by incorporating with a regularization technique. The numerical behavior of our method is also illustrated in comparison with several other methods.

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Acknowledgements

The authors sincerely thank the Editor and anonymous reviewers for their constructive comments which helped them to improve the quality and presentation of this paper. This research 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. Department of Basic Sciences, University of Air Force, Nha Trang, Vietnam

    Pham Kim Quy

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  1. Dang Van Hieu
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Correspondence to Dang Van Hieu.

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Van Hieu, D., Quy, P.K. One-Step iterative method for bilevel equilibrium problem in Hilbert space. J Glob Optim 85, 487–510 (2023). https://doi.org/10.1007/s10898-022-01207-2

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