Strong convergence of an inertial Tseng's extragradient algorithm for pseudomonotone variational inequalities with applications to optimal control problems

TL;DR

This paper introduces a new inertial Tseng's extragradient algorithm for pseudomonotone variational inequalities, demonstrating strong convergence without prior Lipschitz constant knowledge, and applies it to optimal control problems.

Contribution

It proposes a novel inertial extragradient algorithm with a new step size that converges strongly without needing prior Lipschitz constants or extra projections.

Findings

Algorithm converges strongly without prior Lipschitz constant knowledge.

Computational tests show the algorithm's reliability and advantages.

Application to optimal control problems demonstrates practical effectiveness.

Abstract

We investigate an inertial viscosity-type Tseng's extragradient algorithm with a new step size to solve pseudomonotone variational inequality problems in real Hilbert spaces. A strong convergence theorem of the algorithm is obtained without the prior information of the Lipschitz constant of the operator and also without any requirement of additional projections. Finally, several computational tests are carried out to demonstrate the reliability and benefits of the algorithm and compare it with the existing ones. Moreover, our algorithm is also applied to solve the variational inequality problem that appears in optimal control problems. The algorithm presented in this paper improves some known results in the literature.