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A Proximal-Type Algorithm with Bregman Distance for Solving Equilibrium Problems

Author

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  • Grace Nnennaya Ogwo

    (Zhejiang Normal University)

  • Olawale Kazeem Oyewole

    (Tshwane University of Technology)

  • Liya Liu

    (Fuzhou University)

Abstract

In this paper, using the Bregman distance technique, we introduce a proximal-type algorithm for solving equilibrium problems when the bifunction is pseudomonotone in real Hilbert spaces. The proposed algorithm involves only one strongly convex minimization subproblem, which makes our algorithm more effective than some existing algorithms in the literature. Under certain standard assumptions, we obtain a weak convergence result using the proposed algorithm. Finally, we present numerical experiments to illustrate the performance and applicability of our proposed algorithm.

Suggested Citation

  • Grace Nnennaya Ogwo & Olawale Kazeem Oyewole & Liya Liu, 2025. "A Proximal-Type Algorithm with Bregman Distance for Solving Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 207(1), pages 1-24, October.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:1:d:10.1007_s10957-025-02764-8
    DOI: 10.1007/s10957-025-02764-8
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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. Matthew K. Tam & Daniel J. Uteda, 2023. "Bregman-Golden Ratio Algorithms for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 199(3), pages 993-1021, December.
    3. Boţ, R.I. & Csetnek, E.R. & Vuong, P.T., 2020. "The forward–backward–forward method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces," European Journal of Operational Research, Elsevier, vol. 287(1), pages 49-60.
    4. Yonghong Yao & Abubakar Adamu & Yekini Shehu & Jen-Chih Yao, 2024. "Simple proximal-type algorithms for equilibrium problems," Journal of Global Optimization, Springer, vol. 89(4), pages 1069-1098, August.
    5. 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.
    6. Jun Yang & Hongwei Liu, 2020. "A self-adaptive method for pseudomonotone equilibrium problems and variational inequalities," Computational Optimization and Applications, Springer, vol. 75(2), pages 423-440, March.
    7. Dang Hieu, 2017. "New subgradient extragradient methods for common solutions to equilibrium problems," Computational Optimization and Applications, Springer, vol. 67(3), pages 571-594, July.
    Full references (including those not matched with items on IDEAS)

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