A reconsideration of quasimonotone variational inequality problems

TL;DR

This paper analyzes the convergence of Tseng's exgradient algorithm for quasimonotone variational inequality problems, providing new theoretical insights and numerical validation under specific operator conditions.

Contribution

It extends existing results by establishing convergence properties of the algorithm for quasimonotone and Lipschitz continuous operators.

Findings

Proven strong convergence of the algorithm.

Established sublinear and Q-linear convergence rates.

Numerical experiments confirm the effectiveness of the proposed method.

Abstract

This paper is based on Tseng's exgradient algorithm for solving variational inequality problems in real Hilbert spaces. Under the assumptions that the cost operator is quasimonotone and Lipschitz continuous, we establish the strong convergence, sublinear convergence, and Q-linear convergence of the algorithm. The results of this paper provide new insights into quasimonotone variational inequality problems, extending and enriching existing results in the literature. Finally, we conduct numerical experiments to illustrate the effectiveness and implementability of our proposed condition and algorithm.