Inertial Forward-Backward-Forward Method for Non-convex Mixed Variational Inequalities

Abstract

This paper extends inertial forward-backward-forward splitting method already studied by several authors for solving convex variational inequalities to solving non-convex mixed variational inequalities and obtain appropriate convergence results under some conditions. Another contribution is the addition of two-step inertial extrapolation to the forward-backward-forward splitting method to further accelerate the speed of convergence of the method instead of the one-step inertial forward-backward-forward splitting method already studied for convex variational inequalities in the literature. Numerical illustrations are given to confirm the theoretical analysis. 2010 MSC classification: 90C25, 90C30, 90C60, 68Q25, 49M25, 90C22