Extragradient Methods for Solving Equilibrium Problems, Variational Inequalities, and Fixed Point Problems. (2nd November 2017)

• Record Type: Journal Article
• Authors: Jouymandi, Zeynab; Moradlou, Fridoun
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 11(2017)
• Page Start: 1391
• Page End: 1409
• Publication Date: 2017-11-02
• Subjects: Generalized equilibrium problem -- generalized metric projection -- relatively nonexpansive mapping -- strong convergence -- variational inequality; Primary: 47J05 -- 47J20 -- 47J25 -- 47H10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1321017
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, we propose the new extragradient algorithms for an α -inverse-strongly monotone operator and a relatively nonexpansive mapping in Banach spaces. We prove convergence theorems by this methods under suitable conditions. Applying our algorithms, we find a zero paint of maximal monotone operators. Using FMINCON optimization toolbox in MATLAB, we give an example to illustrate the usability of our results.