Improved inertial extragradient methods for solving pseudo-monotone variational inequalities

Abstract

Thong et al. (A strong convergence theorem for Tseng's extragradient method for solving variational inequality problems. Optim Lett. 2020;14:1157–1175) introduced inertial Tseng's extragradient method to variational inequality problems for monotone and Lipschitz continuous mappings. In this work, we extend this method for solving variational inequality problems with pseudo-monotone and Lipschitz continuous mappings in real Hilbert spaces. The first algorithm provides the strong convergence without using the viscosity technique, as well as the monotonicity of the associated mapping. The advantage of the second algorithm is that it does not require the knowledge of the Lipschitz constants of the variational inequality mappings. Finally, some numerical experiments illustrating the performance of our algorithms are discussed.