A non-interior-point smoothing algorithm for the nonlinear complementarity problem with a P* function

A smoothing function is used to reformulate the P_* nonlinear complementarity problem (P_* NCP) as a parameterized smooth equation which can be solved by a non-interior-point smoothing method. Under an assumption that the P_* NCP has a nonempty solution set, the proposed algorithm is proved to be globally convergent and the iteration sequence generated by the proposed algorithm is bounded. Furthermore, this assumption is weaker than the ones used in most existing smoothing algorithms. Without any additional assumption, the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P_* NCP.