Weak Convergence for Variational Inequalities with Inertial-Type Method

TL;DR

This paper introduces an inertial projection method for solving variational inequalities with non-Lipschitz monotone functions, demonstrating weak convergence and improved efficiency through theoretical analysis and numerical tests.

Contribution

It presents a novel inertial projection-type algorithm with weak convergence guarantees for non-Lipschitz monotone variational inequalities, expanding existing methods.

Findings

The proposed method converges weakly under certain conditions.

Numerical tests show improved efficiency over existing methods.

The method is effective for non-Lipschitz monotone problems.

Abstract

Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give weak convergence analysis under appropriate conditions. Some test results are performed and compared with relevant methods in the literature to show the efficiency and advantages given by our proposed methods.