Convergence Analysis of the Self-Adaptive Projection Method for Variational Inequalities with Non-Lipschitz Continuous Operators

TL;DR

This paper introduces a self-adaptive projection method for solving variational inequalities with non-Lipschitz operators, providing convergence analysis and demonstrating its effectiveness through numerical experiments.

Contribution

It develops a novel self-adaptive stepsize approach for variational inequalities with non-Lipschitz operators, extending existing methods without requiring Lipschitz continuity.

Findings

Method converges under mild assumptions.

Numerical experiments show the method's effectiveness.

Outperforms traditional approaches in tests.

Abstract

In this paper, we employ Tseng's extragradient method with the self-adaptive stepsize to solve variational inequality problems involving non-Lipschitz continuous and quasimonotone operators in real Hilbert spaces. The convergence of the proposed method is analyzed under some mild assumptions. The key advantages of the method are that it does not require the operator associated with the variational inequality to be Lipschitz continuous and that it adopts the self-adaptive stepsize. Numerical experiments are also provided to illustrate the effectiveness and superiority of the method.