An Inertial Extragradient Algorithm for Solving Variational Inequalities

In this paper, we introduce a new extragradient algorithm for solving variational inequality problems involving pseudomontone with Lipschitz continuous operators. The algorithm which combines the inertial technique and the extragradient algorithm. We show that the algorithm is globally convergence without any knowledge of the Lipschitz constant of the mapping. Besides, linear convergence is guaranteed under additional strong pseudo-monotonicity. Finally, compared with other algorithms, the numerical results indicate that our algorithm has a better behavior.