New Double Projection Algorithms For Pseudomonotone Variational Inequalities

In this thesis,the pseudomonotone variational inequality problems are consid-ered in the finite dimensional space Rⁿ.By constructing some hyperplanes which are different from the previous ones,some double projection algorithms for solving single-valued variational inequalities and set-valued variational inequalities are proposed,respectively.First,for the single-valued variational inequality problems,a double projection algorithm is given by constructing a hyperplane which is different from the previous ones.The conver-gence of the algorithm is obtained when the mappingsatisfies the conditions of pseudomono-tone and continuous.Furthermore,if the mappingis Lipschitz continuous,the convergence rate of the algorithm is analyzed when the error bound condition is satisfied.Numerical exper-iments are presented to show the effectiveness of the proposed algorithm.Then,for the set-valued variational inequality problems,a double projection algorithm is proposed by constructing a hyperplane which is different from those in the existing literature.The convergence theorem of the algorithm is given when the set-valued mappingis pseu-domonotone and continuous and has nonempty compact convex values.Furthermore,if the set-valued mappingis Lipschitz continuous,the convergence rate of the algorithm is ana-lyzed under the condition that the error bound is satisfied.Numerical experiments are given to illustrate the effectiveness of the proposed algorithm.