A regularization Newton method based on the generalized Fischer–Burmeister smoothing function for the NCP

Abstract

Based on the generalized Fischer–Burmeister smoothing function, we propose a regularization Newton method for solving the nonlinear complementarity problem. The proposed method views the regularization parameter as an independent variable. Moreover, it solves a perturbed Newton equation to obtain the search direction and adopts a simple nonmonotone line search scheme to improve the numerical results. Under suitable assumptions, we prove that our method has global and local quadratic convergence and the regularization parameter converges to zero globally Q-linearly. Numerical results shows that there does exist new smoothing function which is better than the Fischer–Burmeister smoothing function.