Forward-Reflected-Backward Algorithms with Double Inertial Extrapolations for Variational Inequalities with Applications to Image Processing

Abstract This paper designs forward-reflected-backward algorithms with two inertial extrapolation steps to solve variational inequalities of quasi-monotone operators. We consider forward-reflected algorithms with two inertial extrapolation steps for constant and non-decreasing self-adaptive step sizes. The algorithms also feature one projection and operator evaluation at each inertial step per iteration. We give weak convergence results for the two proposed algorithms. Strong convergence and linear convergence results are also achieved under standard conditions. Numerical results from image processing confirm the superiority of our algorithms over other related ones in the literature. 2020 MSC classification: 47H05, 47J20, 47J25, 65K15, 90C25.