Convergence Analysis of Projection Method for Variational Inequalities

Yekini Shehu, Olaniyi. S. Iyiola, Xiao-Huan Li, Qiao-Li Dong

Published 2021-01-22Version 1

The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is monotone and uniformly continuous. We carry out a unified analysis of the proposed method under very mild assumptions. In particular, weak convergence of the generated sequence is established and nonasymptotic $O(1/n)$ rate of convergence is established, where $n$ denotes the iteration counter. We also present some experimental results to illustrate the profits gained by introducing the inertial extrapolation steps.