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A novel framework for solving pseudomonotone equilibrium and fixed point problems using bregman techniques
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DOI：10.1007/s44146-025-00220-7.png)
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Abstract
En 中文
The application of a Bregman subgradient extragradient algorithm to pseudomonotone equilibrium and fixed points problems associated with quasi-Bregman nonexpansive mappings is considered. We incorporate a Bregman distance framework and an inertial extrapolation technique to approximate a common solution to both the equilibrium problem and the fixed points of quasi-Bregman nonexpansive mappings within a reflexive Banach space. In addition, we introduce a regulating parameter, denoted by eta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}, to regulate and enhance the step size of the algorithm such that the cost operator does not rely on the Lipschitz constant. We verify the accuracy and effectiveness of our approach with two numerical examples. We note that the incorporation of our parameter eta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document} improves the convergence rate compared to other algorithms. Also, we observed that the smaller the value of eta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}, the faster the convergence. These results demonstrate the effectiveness of our algorithm and provide contributions that advance existing knowledge in this research domain.
Keywords:
Bifunction
Subgradient-extragradient method
Equilibrium problems
Common fixed point
Halpern method
Inertial parameter
Pseudomonotone bifunction
Bregman quasi-nonexpansive mapping
Journal
A
IF:
0.6
Papers:
50
Citations:
0