Convergence Theorem for Variational Inequality in Hilbert Spaces with Applications
Zenn-Tsun Yu, Chih-Sheng Chuang, Lai-Jiu Lin · Numerical Functional Analysis and Optimization · 2018
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.