Quasi-Inertial Tseng's Extragradient Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Quasi-Nonexpansive Operators. (26th December 2020)

• Record Type: Journal Article
• Authors: Zhao, Tu-Yan; Wang, Dan-Qiong; Ceng, Lu-Chuan; He, Long; Wang, Chun-Yan; Fan, Hong-Ling
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 1(2021)
• Page Start: 69
• Page End: 90
• Publication Date: 2020-12-26
• Subjects: Adaptive stepsizes -- fixed point problem -- quasi-inertial Tseng's extragradient algorithms -- variational inequality problem; 47H09 -- 49J40 -- 47J20 -- 47J25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1867866
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In a real Hilbert space, let the VIP indicate a variational inequality problem with Lipschitzian, pseudomonotone operator, and let the FPP denote a fixed-point problem of a quasi-nonexpansive operator with a demiclosedness property. This article designs two quasi-inertial Tseng's extragradient algorithms with adaptive stepsizes for finding a common solution of the VIP and FPP. The proposed algorithms are based on inertial Tseng's extragradient approach with adaptive stepsizes, hybrid steepest-descent algorithm, and viscosity approximation technique. Under appropriate assumptions, it is proven that the sequences constructed by the proposed algorithms converge strongly to a common solution of the VIP and FPP. Finally, the main results are applied to deal with the VIP and FPP in an illustrating example.