An inertial modified algorithm for solving variational inequalities

¹ Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
² Department of Mathematics, College of Air Force, Nha Trang City, Vietnam

^* Corresponding author: dangvanhieu@tdtu.edu.vn, dv.hieu83@gmail.com

Abstract

The paper deals with an inertial-like algorithm for solving a class of variational inequality problems involving Lipschitz continuous and strongly pseudomonotone operators in Hilbert spaces. The presented algorithm can be considered a combination of the modified subgradient extragradient-like algorithm and inertial effects. This is intended to speed up the convergence properties of the algorithm. The main feature of the new algorithm is that it is done without the prior knowledge of the Lipschitz constant and the modulus of strong pseudomonotonicity of the cost operator. Several experiments are performed to illustrate the convergence and computational performance of the new algorithm in comparison with others having similar features. The numerical results have confirmed that the proposed algorithm has a competitive advantage over the existing methods.