Double inertial Forward–Backward–Forward method with adaptive step-size for variational inequalities with quasi-monotonicity

The paper introduce a new inertial forward–backward–forward method with adaptive step size constructed by double inertial extrapolation steps and relaxations to solve variational inequalities with quasi-monotonicity in real Hilbert spaces. We obtain weak and strong convergence results for our propose inertial Forward–Backward–Forward method under some mild conditions. Linear convergence results under a special case of our proposed method are given. Preliminary numerical results show that our proposed method is competitive with other related methods in the literature.