Linear Convergence Results for Inertial Type Projection Algorithm for Quasi-Variational Inequalities

TL;DR

This paper introduces a new inertial gradient projection algorithm for quasi-variational inequalities in Hilbert spaces, establishing its linear convergence rate and demonstrating its effectiveness through numerical experiments.

Contribution

The paper develops a novel inertial gradient projection algorithm with proven linear convergence for quasi-variational inequalities, filling a gap in existing research.

Findings

Proven linear convergence rate for the proposed algorithm.

Numerical results show competitive performance compared to existing methods.

Algorithm effectively handles strongly monotone and Lipschitz continuous operators.

Abstract

Many recently proposed gradient projection algorithms with inertial extrapolation step for solving quasi-variational inequalities in Hilbert spaces are proven to be strongly convergent with no linear rate given when the cost operator is strongly monotone and Lipschitz continuous. In this paper, our aim is to design an inertial type gradient projection algorithm for quasi-variational inequalities and obtain its linear rate of convergence. Therefore, our results fill in the gap for linear convergence results for inertial type gradient projection algorithms for quasi variational inequalities in Hilbert spaces. We perform numerical implementations of our proposed algorithm and give numerical comparisons with other related inertial type gradient projection algorithms for quasi variational inequalities in the literature.