Convergence Analysis of Modified Bregman Extragradient Method for Variational Inequality Problems

Qingqing Fu (), Gang Cai (), Kunrada Kankam () and Prasit Cholamjiak ()
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Qingqing Fu: Chongqing Normal University
Gang Cai: Chongqing Normal University
Kunrada Kankam: Faculty of Education, Suan Dusit University, Lampang Center
Prasit Cholamjiak: University of Phayao

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 3, No 20, 34 pages

Abstract: Abstract In this paper, we put forward a modified extragradient method with Bregman divergence and a novel stepsize rule for solving pseudo-monotone variational inequality problems in reflexive Banach spaces, this new stepsize is the combination of self-adjustment stepsize and line-search stepsize. Under some suitable constraints imposed on the operators and parameters, we establish a strong convergence theorem for the proposed algorithm. In addition, we give two new algorithms in a real Hilbert space: a Tseng-type method and a subgradient extragradient method, and prove their weak convergence and R-linear convergence results. Moreover, our algorithms do not require prior knowledge of Lipschitz constant for the operators. Finally, some numerical experiments are given to illustrate the performance of our proposed algorithms.

Keywords: Bregman distance; Variational inequality; Strong convergence; Pseudo-monotone operator; Reflexive Banach spaces; 47H05; 47H07; 47H10; 54H25 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02822-1

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