Convergence Theorem for Variational Inequality in Hilbert Spaces with Applications. (11th June 2018)

• Record Type: Journal Article
• Authors: Yu, Zenn-Tsun; Chuang, Chih Sheng; Lin, Lai-Jiu
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 8(2018)
• Page Start: 865
• Page End: 893
• Publication Date: 2018-06-11
• Subjects: Linear inverse problem -- minimization problem -- split feasibility problem -- strongly monotone mapping -- variational inequality; 47H09 -- 47J20 -- 49J30 -- 90C33; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1424201
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, we study variational inequality over the set of the common fixed points of a countable family of quasi-nonexpansive mappings. To tackle this problem, we propose an algorithm and use it to prove a strong convergence theorem under suitable conditions. As applications, we study variational inequality over the solution set of different nonlinear or linear problems, like minimization problems, split feasibility problems, convexly pseudoinverse problems, convex linear inverse problems, etc.