A family of smooth ncp functions and an inexact levenberg-marquardt method for nonlinear complementarity problems

. In this paper, we introduce a family of new NCP functions which is smooth, coercive and strongly semismooth. Based on new NCP functions, we propose an inexact Levenberg-Marquardt method for solving Nonlinear Complementarity Problem (NCP). Different from existing exact/inexact LevenbergMarquardt methods, the proposed method adopts a derivative-free line search to ensure its globalization. Moreover, by using the strong semismoothness of new NCP functions, we prove that the proposed method is locally superlinearly/quadratically convergent under a local error bound condition. Some numerical results are reported.