A Smooth Nonlinear Complementarity Method For Solving The Problem

For the nonlinear complementarity problem, a new smoothing approximate function of the Fischer-Burmeister function is built and its property is given. The smoothing Newton method is improved. The convergence of the new method is proved. The numerical results also show that the proposed smoothing Newton algorithm works well for these tested problems in this paper.In the first chapter, some necessary and essential knowledge of the nonlinear complementarity problem is introduced. The related theory of the nonlinear complementarity problem’s solutions and the essential solving method of the nonlinear complementarity problem is given.For the nonlinear complementarity problem, the basic principle and basic property of the smoothing Newton method is introduced in the second chapter. A new smoothing approximate function of the Fischer-Burmeister function is built and its properties and theorems is given.In the last chapter, The nonlinear complementarity problem is transformed to a system of smooth equations by the new smoothing function of NCP function. The improved smoothing Newton method is proposed for the linear complementarity problem. Under mild assumptions, its global convergence are proved.