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

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.