A new modified extragradient method with line-search process for solving pseudomonotone variational inequality in Hilbert spaces

Abstract

ABSTRACT In this paper, we mainly introduce a new algorithm with a different line-search process for solving variational inequality problem of pseudomonotone and non-Lipschitz operators in real Hilbert spaces. Under some appropriate restrictions imposed on the parameters, we prove a strong convergence theorem for finding an element of solutions of variational inequality problem. At the same time, we give some numerical examples to illustrate the effectiveness of our proposed algorithm. The main results obtained in this paper extend and improve many recent ones in the literature.