New double projection algorithm for solving variational inequalities

We propose a class of new double projection algorithms for solving variational inequality problem,which can be viewed as a framework of the method of solodov and svaiter by adopting a class of new hyperplanes. by the separation property of hyperplane,our method is proved to be globally convergent under very mild assumptions. in addition,we propose a modified version of our algorithm that finds a solution of variational inequality which is also a fixed point of a given nonexpansive mapping. if,in addition,a certain local error bound holds,we analyze the convergence rate of the iterative sequence. numerical experiments prove that our algorithms are efficient. © 2013 lian zheng.