Some new results in the existence and uniqueness of the solution to the variational inequality problem and its application

Abstract

ln this article, we consider the existence and uniqueness of the solution to the variational inequality problems and applying these results to investigate the convergence and the convergent rate of a projection method for solving the problem. At first, we introduce the variational inequality problem in a general setting and some basic definitions. Then, we present normal results about the existence and uniqueness of the solution to this problem. After that, we prove new outcomes about the existence and uniqueness of the variational inequality problem. Finally, new results are used to study the convergence and convergence rate of the projection method to the variational inequality problem.