A Halpern’s Mean Subgradient Extragradient Method for Solving Variational Inequalities

Authors

Keywords:

averaging matrix, subgradient extragradient method, mean value iteration, variational inequalities, strong convergence

Abstract

This paper deals with the solving of a variational inequality problem in a real Hilbert space. To this end, we present a Halpern’s mean
subgradient extragradient method. We prove the strong convergence result of the proposed method under some suitable assumptions of step-size in case of the monotone and Lipschitz continuous operator.

Author Biographies

Apichit Buakird, Department of Mathematics, Faculty of Science, Khon Kaen University

MSc. in Mathematics

Nimit Nimana, Department of Mathematics, Faculty of Science, Khon Kaen University

Associate Profressor at Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Narin Petrot, Department of Mathematics, Faculty of Science, Naresuan University

Professor at Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand and Center of Excellence in Nonlinear Analysis and Optimization, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Porntip Promsinchai, King Mongkut’s University of Technology Thonburi (KMUTT)

Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand

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Published

2022-12-25

How to Cite

Buakird, A., Nimana, N., Petrot, N., & Promsinchai, P. (2022). A Halpern’s Mean Subgradient Extragradient Method for Solving Variational Inequalities. Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications, 1(2), 177–191. Retrieved from https://bangmodjmcs.com/index.php/ncao/article/view/85

Issue

Vol. 1 No. 2 (2022): July - December, 2022

Section

Articles

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Copyright (c) 2022 Apichit Buakird, Nimit Nimana, Narin Petrot, Porntip Promsinchai

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