A smoothing inexact Newton method for nonlinear complementarity problems

In this article, we propose a new smoothing inexact Newton algorithm for solving nonlinear complementarity problems (NCP) base on the smoothed Fischer–Burmeister function. In each iteration, the corresponding linear system is solved only approximately. The global convergence and local superlinear convergence are established without strict complementarity assumption at the NCP solution. Preliminary numerical results indicate that the method is effective for large-scale NCP.