Proximal Point Algorithm For Solving Two Kinds Of Problem

In this thesis,we propose proximal point algorithm for two kinds of problems.One is the inexact proximal point algorithm for the minimization of DC function(difference of two convex function),the other is the relaxation- proximal point algorithm for monotone nonlinear complementity problem.For the minimization of DC function,the conventional methods are ineffective when one of these convex functions is nonsmooth or both are nonsmooth. But the proximal point algorithm is an effective method for solving DC function optimization problems with global convergence,even with superlinear convergence.Inexact proximal point algorithm is more practical than proximal point algorithm. And it can keep the convergence of this method. We use inexact proximal point algorithm for solving the DC function minimization .Moreover,with subgradient and strong convexity ,we can prove the global convergence of inexact proximal point algorithm under the parameter is bounded or unbounded.We also propose relaxation- proximal point algorithm for solving nonlinear monotone complementarity problem. This method is combined the Newton method and proximal point algorithm. It uses general Newton method for solving the subproblem of the original problem, the relaxation- proximal point algorithm to produce the next iteration point. We can prove that under some assumptions the relaxation-proximal point algorithm has global convergence and under further assumptions the relaxation-proximal point algorithm has superlinear convergence.