Error Bound For Solutions Of Variational Inequality Problems

Variational inequality problem is one of the most important part of the optimization area, which has broad and deep application of mechanics, differential equations, control theory, mathematical economics, game theory and nonlinear programming.The variational inequality problem in this paper, we define the optimal value function of trust region subproblem, and study the nature of it. Then we provide global and local error estimates for the feasible point. The paper is divided into five parts as follows:In chapter1, we give a brief description to the existed research work on the variational inequality problems and give an account of the main results of the paper.In chapter2, we state some definition and notations, and then construct the optimal value function in the trust region method for the variational inequality problem.Some properties of the optimal value function is given in chapter3.In chapter4, under strongly monotonic and monotonic conditions, we utilize the optimal value function to ensure some error bounds, which are a global and a local error estimate for a feasible solution.In chapter5, we analysis the convergence and the finite termination of the sequence.