Modified Subgradient Extragradient Algorithms with A New Line-Search Rule for Variational Inequalities

In this paper, we introduce a modified subgradient extragradient algorithm with a new line-search rule for solving pseudomonotone variational inequalities with non-Lipschitz mappings. The new line-search rule is designed by the golden radio (5+1)/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\sqrt{5}+1)/2$$\end{document}. We prove the strong convergence theorem under some appropriate conditions in real Hilbert spaces. Finally, we give some numerical experiments to illustrate the performances and advantages of the proposed algorithm.