THE PROPERTIES OF A NEW SMOOTHING FUNCTION AND A REGULARIZED SMOOTHING NEWTON METHOD FOR THE P0-NCP

In this paper we introduce a new smoothing function by smoothing the Fischer-Burmeister function. This function has coerciveness under suitable conditions which plays an important role in the convergence analysis of smoothing-type methods. Based on this new function, we propose a regularized smoothing Newton method for solving the nonlinear complementarity problem with P0-function. It is proved that the proposed method is globally and locally quadratically convergent in absence of strict complementarity condition at the optimal solution. Some numerical results are reported which indicate the effectiveness of our method.