Strong Convergent Theorems Governed by Pseudo-Monotone Mappings

Abstract

The purpose of this paper is to introduce two different kinds of iterative algorithms with inertial effects for solving variational inequalities. The iterative processes are based on the extragradient method, the Mann-type method and the viscosity method. Convergence theorems of strong convergence are established in Hilbert spaces under mild assumption that the associated mapping is Lipschitz continuous, pseudo-monotone and sequentially weakly continuous. Numerical experiments are performed to illustrate the behaviors of our proposed methods, as well as comparing them with the existing one in literature.

Keywords

• variational inequality
• inertial extrapolation
• pseudomonotonicity
• projection method
• extragradient method