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Optimization and Engineering

Proximal methods for equilibrium problems over the set of fixed points of enriched nonexpansive mappings

  • 12-08-2025
  • Research Article
Published in:
Authors
Natthaya Boonyam
Sani Salisu
Vasile Berinde
Poom Kumam
Published in
Optimization and Engineering | Issue 1/2026

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Abstract

This article delves into the application of proximal methods for solving equilibrium problems, particularly focusing on the set of fixed points of nonexpansive mappings. The study introduces a reflected-proximal method and provides a comprehensive analysis of its convergence properties. Key topics include the formulation of the equilibrium problem, the development of the reflected-proximal algorithm, and the examination of its convergence under various assumptions. The article also explores the application of the method to variational inequality problems and presents numerical illustrations to demonstrate its effectiveness. Additionally, the study compares the proposed method with existing algorithms, highlighting its advantages and potential for future research.
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previous article Checkerboard-free topology optimization for cellular materials via the finite-volume theory
next article Convergence results of proximal-type algorithms with reflections for variational inequalities
Title
Proximal methods for equilibrium problems over the set of fixed points of enriched nonexpansive mappings
Authors
Natthaya Boonyam
Sani Salisu
Vasile Berinde
Poom Kumam
Publication date
12-08-2025
Publisher
Springer US
Published in
Optimization and Engineering / Issue 1/2026
Print ISSN: 1389-4420
Electronic ISSN: 1573-2924
DOI
https://doi.org/10.1007/s11081-025-10008-x
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