An inertial Tseng's extragradient method for solving multi-valued variational inequalities with one projection

TL;DR

This paper proposes an inertial Tseng's extragradient algorithm for multi-valued variational inequalities that requires only one projection per iteration, demonstrating strong convergence and efficiency through numerical tests.

Contribution

It introduces a novel inertial Tseng's extragradient method that reduces computational effort by using only one projection and proves its strong convergence under specific conditions.

Findings

Algorithm converges strongly under pseudomonotonicity.

Numerical results show improved efficiency over existing methods.

Method requires only one projection per iteration.

Abstract

In this paper, we introduce an inertial Tseng's extragradient method for solving multi-valued variational inequalits, in which only one projection is needed at each iterate. We also obtain the strong convergence results of the proposed algorithm, provided that the multi-valued mapping is continuous and pseudomonotone with nonempty compact convex values. Moreover, numerical simulation results illustrate the efficiency of our method when compared to existing methods.