A class of projection and contraction methods for monotone variational inequalities

In this paper we introduce a new class of iterative methods for solving the monotone variational inequalities\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$u* \in \Omega , (u - u*)^T F(u*) \geqslant 0, \forall u \in \Omega .$$ \end{document} Each iteration of the methods presented consists essentially only of the computation ofF(u), a projection to Ω,v:=PΩ[u-F(u)], and the mappingF(v). The distance of the iterates to the solution set monotonically converges to zero. Both the methods and the convergence proof are quite simple.