Weak convergence of projection algorithm with momentum terms and new step size rule for quasimonotone variational inequalities

TL;DR

This paper introduces a modified projection algorithm with momentum and a novel step size rule for solving quasimonotone variational inequalities, proving its weak convergence under certain conditions and demonstrating its effectiveness through experiments.

Contribution

It proposes a new projection method with momentum and an increasing step size strategy, establishing weak convergence for quasimonotone Lipschitz operators.

Findings

Algorithm converges weakly under specified conditions.

Numerical experiments show improved efficiency.

Application to signal recovery demonstrates practical utility.

Abstract

This article analyses the simple projection method proposed by Izuchukwu et al. [8, Algorithm 3.2] for solving variational inequality problems by incorporating momentum terms. A new step size strategy is also introduced, in which the step size sequence increases after a finite number of iterations. Under the assumptions that the underlying operator is quasimonotone and Lipschitz continuous, we establish weak convergence of the proposed method. The effectiveness and efficiency of the algorithm are demonstrated through numerical experiments and are compared with existing approaches from the literature. Finally, we apply the proposed algorithm to a signal recovery problem.