Analysis of relaxed inertial method for non-convex mixed variational inequalities

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. Next, we propose another inertial forward-backward-forward splitting method for which the inertial factor θ is chosen in [0, 1] with θ = 1 possible. As far as we know, the choice θ = 1 has not been considered before in the literature for inertial forward-backward-forward splitting method for solving non-convex mixed variational inequalities. Numerical illustrations are given to confirm the theoretical analysis.