An Approximation Method For Solving Nonlinear Complementarity Problems

We studied the numerical method for solving nonlinear complementarity problems in this paper. The numerical method is smoothing method, which is employed smoothing approximate function. This article consists of three parts.In the first chapter, some related basic knowledge is introduced, including relevant definition and conclusion of P₀-matrix, basic knowledge and propositions of nonlinear complementarity problem.A new smoothing approximate function is given in the second chapter. Some properties of this function are studied. A system of equations is transformed based on the new smoothing approximate function. Its properties are proposed. Present a new smoothing method based on the new smoothing approximate function. The convergence of nonlinear complementarity problem is proved, and numerical results are given.In the third chapter, an improved algorithm is given, in which the direction d_k is different. And a non-monotone line search is used in the algorithm. So the algorithm can be used to solve the general nonlinear complementarity problems. The convergence of nonlinear complementarity problem is proved under mild conditions, and numerical results are given.