Quasi-Inertial Tseng's Extragradient Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Quasi-Nonexpansive Operators. (26th December 2020) - Zhao, Tu-Yan; Wang, Dan-Qiong; Ceng, Lu-Chuan; He, Long; Wang, Chun-Yan; Fan, Hong-Ling
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.