A self-adaptive subgradient extragradient method with conjugate gradient-type direction for pseudomonotone variational inequalities

TL;DR

This paper proposes a self-adaptive subgradient extragradient method with a conjugate gradient-type direction for solving pseudomonotone variational inequalities, improving convergence speed and robustness without requiring prior knowledge of Lipschitz constants.

Contribution

It introduces a novel self-adaptive algorithm incorporating conjugate gradient directions for pseudomonotone variational inequalities, with proven strong convergence and demonstrated computational advantages.

Findings

Algorithm converges strongly to the solution set.

Numerical experiments show improved efficiency and robustness.

Eliminates the need for Lipschitz constant knowledge.

Abstract

This paper introduces a subgradient extragradient algorithm with a conjugate gradient-type direction to solve pseudomonotone variational inequality problems in Hilbert spaces. The algorithm features a self-adaptive strategy that eliminates the need for prior knowledge of the Lipschitz constant and incorporate a conjugate gradient-type direction to enhance convergence speed. We establish a result describing the behavior generated therefrom toward the solution set. Using this result, we prove the strong convergence of the proposed method and provide numerical experiments to demonstrate its computational efficacy and robustness.