A Forward-Backward-Forward Algorithm for Solving Quasimonotone Variational Inequalities-Reference-Cited by-同舟云学术

A Forward-Backward-Forward Algorithm for Solving Quasimonotone Variational Inequalities

Published:2022-01-04 Issue: Volume:2022 Page:1-8
ISSN:2314-8888
Container-title:Journal of Function Spaces
language:en
Short-container-title:Journal of Function Spaces

Author:

Yin Tzu-Chien¹^ORCID,Hussain Nawab²^ORCID

Affiliation:

1. Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

2. Department of Mathematics, King Abdulaziz University, P.O. Box 80203 Jeddah 21589, Saudi Arabia

Abstract

In this paper, we continue to investigate the convergence analysis of Tseng-type forward-backward-forward algorithms for solving quasimonotone variational inequalities in Hilbert spaces. We use a self-adaptive technique to update the step sizes without prior knowledge of the Lipschitz constant of quasimonotone operators. Furthermore, we weaken the sequential weak continuity of quasimonotone operators to a weaker condition. Under some mild assumptions, we prove that Tseng-type forward-backward-forward algorithm converges weakly to a solution of quasimonotone variational inequalities.

Publisher

Hindawi Limited

Subject

Analysis

Link

http://downloads.hindawi.com/journals/jfs/2022/7117244.pdf

Reference53 articles.

1. Formes bilineaires coercivites surles ensembles convexes;G. Stampacchi;Comptes Rendus Hebdomadaires Des Seances De L Academie Des Sciences,1964

2. Iterative algorithms for split equilibrium problems of monotone operators and fixed point problems of pseudo-contractions

3. Convex Analysis and Monotone Operator Theory in Hilbert Spaces

4. Numerical Methods for Nonlinear Variational Problems

5. Convex programming in Hilbert space

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