A new inertial double-projection method for solving variational inequalities

Abstract

In this paper, we introduce a new algorithm of inertial form for solving monotone variational inequalities (VI) in real Hilbert spaces. Motivated by the subgradient extragradient method, we incorporate the inertial technique to accelerate the convergence of the proposed method. Under standard and mild assumption of monotonicity and Lipschitz continuity of the VI associated mapping, we establish the weak convergence of the scheme. Several numerical examples are presented to illustrate the performance of our method as well as comparing it with some related methods in the literature.