Work

Projected reflected gradient method with momentum terms for variational inequalities

Year: 2025

Type: article

Abstract: In this paper, we propose a projected reflected gradient method with momentum terms for solving variational inequality problems in Hilbert spaces. The proposed method involves only one projection onto the feasible set and one operator evaluation per iteration. Under certain standard assumptions, we establish the weak convergence of the proposed method. Furthermore, we also establish the linear convergence result when the operator is strongly monotone and Lipschitz continuous. Finally, we present numerical experiments to show that the projected reflected gradient method with momentum terms outperforms some related methods in the literature for solving variational inequality problems.

Source: Numerical Algebra Control and Optimization

DOI: 10.3934/naco.2025027

Authors: Grace Ogwo, Chinedu Izuchukwu, Olawale Oyewole, Yekini Shehu, Jen-Chih Yao

Institutions: Zhejiang Normal University, University of the Witwatersrand, Tshwane University of Technology, China Medical University

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Zhejiang Normal University

Award: G219214856