Outer approximation methods for solving variational inequalities in Hilbert space

• Published in: Optimization Vol. 66; no. 3; pp. 417 - 437
• Main Authors: Gibali, Aviv, Reich, Simeon, Zalas, Rafał
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 04.03.2017; Taylor & Francis LLC
• Subjects: Approximation; Common fixed point; Convergence; Cutters; Hilbert space; Inequalities; iterative method; Iterative methods; Mathematical analysis; Operators; Optimization; Quantum theory; quasi-nonexpansive operator; subgradient projection; variational inequality

In this paper, we study variational inequalities in a real Hilbert space, which are governed by a strongly monotone and Lipschitz continuous operator F over a closed and convex set C. We assume that the set C can be outerly approximated by the fixed point sets of a sequence of certain quasi-nonexpan...