New inertial forward-backward type for variational inequalities with Quasi-monotonicity

• Published in: Journal of global optimization Vol. 84; no. 2; pp. 441 - 464
• Main Authors: Izuchukwu, Chinedu, Shehu, Yekini, Yao, Jen-Chih
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2022; Springer; Springer Nature B.V
• Subjects: Computer Science; Convergence; Hilbert space; Inequalities; Iterative methods; Mathematical programming; Mathematics; Mathematics and Statistics; Methods; Operations Research/Decision Theory; Optimization; Real Functions; Weak convergence; Quasi-monotone; Linear convergence; 65K15; 47J20; Inertial projection method; 90C25; Hilbert spaces; 47H05; 47J25; Variational inequalities

In this paper, we present a modification of the forward-backward splitting method with inertial extrapolation step and self-adaptive step sizes to solve variational inequalities in a quasi-monotone setting. Our proposed method involves one computation of the projection onto the feasible set and one...