Self adaptive inertial extragradient algorithms for solving variational inequality problems

TL;DR

This paper introduces self-adaptive inertial extragradient algorithms for variational inequality problems, demonstrating strong convergence without prior knowledge of the Lipschitz constant, supported by numerical experiments.

Contribution

It proposes new self-adaptive inertial extragradient algorithms with proven strong convergence for variational inequalities, eliminating the need for prior Lipschitz constant knowledge.

Findings

Algorithms converge strongly without prior Lipschitz constant knowledge

Numerical experiments show competitive performance

Comparison with existing methods highlights advantages

Abstract

In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for our algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performances of the proposed algorithms and provide a comparison with related ones.