An improved subgradient extragradient self-adaptive algorithm based on the golden ratio technique for variational inequality problems in Banach spaces

Abstract

We investigate the iterative approximation of solutions to the variational inequality problem (VIP) in Banach spaces. We propose a subgradient extragradient self-adaptive algorithm based on the golden ratio technique for solving the VIP associated with a pseudomonotone cost operator. By utilizing the Bregman distance function and Bregman generalized projection, we establish a weak convergence result to a solution of the VIP. Notably, our proposed method does not require prior knowledge of the Lipschitz constant of the associated operator. Additionally, we present some numerical results and made comparisons with previous methods. Our findings extend and generalize previously reported results in the literature on this topic.