Nonmonotone smoothing inexact Newton method for the nonlinear complementarity problem

Smoothing Newton methods have been successfully applied to solve the nonlinear complementarity problem (NCP). In this paper, we first study some properties of the generalized Fischer–Burmeister smoothing function. Based on this function, we then design a smoothing inexact Newton method for the NCP. At each iteration, a system of linear equations is solved only inexactly. Moreover, our method uses a nonmonotone line search technique which is much simpler than existing nonmonotone line searches used in smoothing Newton methods. Under suitable assumptions, we prove that the proposed method is globally and locally superlinearly convergent. Some numerical results are also reported.