The Properties of a New Smoothing Function and a Modified Smoothing Newton Method for the P0-NCP

In this paper we introduce a new smoothing function which has many nice properties. Based on this function,a smoothing Newton method is proposed to solve the nonlinear complementarity problem with P0-function(denoted by P0-NCP). Our method adopts a variant merit function. Moreover, we use a modified Newton equationto obtain the search direction. Under suitable assumptions, we show that the proposed method is globally andlocally quadratically convergent. Some preliminary computational results are reported.