Trust Region Method For Variational Inequality Problem

Trust region method is a kind of efficient and robust method to solve general unconstrained optimization. But the choice of the trust region radius is very important to the efficiency of the method. Recently Zhang proposed a new trust region method called adaptive trust region method, in which the trust region radius depends on the gradient and Hesse matrix information of the current iterate point. Numerical results show the efficiency of the method. This thesis tombines the nonmonotone technique to the adaptive trust region method, adaptive nonmonotonic trust region algorithm for unconstrained optimization is improved, it takes nonmonotonic linear search instead of resolving the subproblem when the trail step is not successful. This may allow a considerable computational saving. Due to particularity of trust region's radius, the paper is not only proved that at least a accumulation point is stability but also that any accumulation point produced by this algorithm is stability for unconstrained optimization. In addition, global convergence is proved under certain conditions.This thesis is not only to linearize variational inequality but also linearize set of constraints. Constraints to put a special kind of non-empty closed convex variational inequalities into the equivalent of a muli-faceted set of constraints of linear convex variational inequalities, we calculate it using projection and contraction method.This paper convert boxed variational inequality into an equivalent unconstrained optimization problem, and then solve it using trust region method.