A SELF-ADAPTIVE INERTIAL EXTRAGRADIENT ALGORITHM FOR SOLVING PSEUDO-MONOTONE VARIATIONAL INEQUALITIES IN HILBERT SPACES

In this paper, we study the variational inequality involving pseudomonotone and Lipschitz continuous mappings in real Hilbert spaces. We present a self-adaptive iterative method which combines the inertial technique and the Tseng's extragradient idea with a Armijo-like step size rule. The construction of our algorithm is without the prior knowledge of the Lipschitz constant of the cost operators. Moreover, we also give some numerical experiments to demonstrate the efficiency of our algorithm by comparing with existing ones.