Some Hyperplane Projection Methods For Two Kinds Of Variational Inequalities

In this thesis,two types of hyperplane projection algorithms corresponding to single-valued and multi-valued variational inequality in finite dimensional space are proposed respectively.The hyperplane projection algorithms aim at finding a hyperplane separating the current iterative point and the solution set of variational inequality problem,which usually can be used for solving pseudo-monotone variational inequality.In recent years,some authors present a version of hyperplane projection algorithms for solving variational inequality without monotonicity.Based on projection and contraction method,we construct a novel hyperplane and introduce a new hyperplane projection algorithm for solving pseudo-monotone variational inequalities in chapter 2.If the solution of variational inequality does exist and F is a continuous and pseudo-monotone mapping,the sequence produced by our method globally converges to a solution.Once a certain error bound holds,the convergence rate of the iterative sequence is established.Numerical experiments at the end of the chapter indicate our algorithm needs less iterates than other four algorithms in some cases.In chapter 3,a new hyperplane projection algorithm for solving multi-valued variational inequalities without monotonicity is presented.If the dual problem has a solution,the whole sequence converges to a solution of the variational inequality.Instead of the linesearch and hyperplane used in [27],we adopt different kinds of linesearch and halfspaces in our algorithm.We compare our algorithm with the algorithm in [27] by the numerical experiments which show that less iterates are needed by using our method.