Modified Newton-type methods for the NCP by using a class of one-parametric NCP-functions

摘要

In this paper, we propose a new Newton-type method for solving the nonlinear complementarity problem (NCP) based on a class of one-parametric NCP-functions, where an approximate Newton direction can be obtained by solving a modified Newton equation in each iteration. The method is shown to be globally convergent without any additional assumption. To investigate the fast convergence of this class of methods, we propose a modified version of the proposed method and show the method is globally and locally superlinearly convergent. The preliminary numerical results show the effectiveness of the modified method.