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

Grace Nnennaya Ogwo (), Olawale Kazeem Oyewole () and Liya Liu ()
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Grace Nnennaya Ogwo: Zhejiang Normal University
Olawale Kazeem Oyewole: Tshwane University of Technology
Liya Liu: Fuzhou University

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 1, No 7, 24 pages

Abstract: 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.

Keywords: Equilibrium problems; Bregman distance; Proximal-type algorithm; Pseudomonotone bifunction; Weak convergence; 68Q25; 90C60; 90C30; 90C25 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02764-8

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