Forward-reflected-backward method with two-step inertial for variational inequalities

A forward-reflected-backward splitting method of Malitsky-Tam with two-step inertial extrapolation and self-adaptive step sizes is proposed to solve variational inequalities in quasi-monotone setting.Our method features one projection onto the feasible set and one functional evaluation at each iteration.A two-step inertial extrapolation is added to further improve on the convergence speed of the proposed method and self-adaptive step sizes are used in order to reduce computational complexity of our method.Weak convergence analysis are obtained under some easy to verify conditions on the iterative parameters in Hilbert spaces.Preliminary numerical tests are performed to support the theoretical analysis and show the superiority of our method over recent related methods in the literature.