Weak and strong convergence of inertial Tseng's extragradient algorithms for solving variational inequality problems

Abstract

In this paper, we introduce two inertial Tseng's extragradient algorithms with the Armijo-like step size rule for solving variational inequality problems involving monotone and Lipschitz continuous operators. Strong and weak convergence theorems are established in Hilbert spaces. Some numerical experiments are provided to illustrate the efficiency and advantage of the proposed algorithms.