A smoothing Levenberg-Marquardt method for NCP

In this paper, we convert the nonlinear complementarity problems to an equivalent smooth nonlinear equation system by using smoothing technique. Then we use Levenberg-Marquardt type method to solve the nonlinear equation system. The method has the following merits: (i) any cluster point of the iteration sequence is a solution of the P0 − NCP; (ii) it generates a bounded sequence if the P0 − NCP has a nonempty and bounded solution set; (iii) if the generalized Jacobian is nonsingular at a solution point, then the whole sequence converges to the (unique) solution of the P0 − NCP superlinearly; (iv) for the P0 − NCP, if an accumulation point of the iteration sequence satisfies strict complementary condition, then the whole sequence converges to this accumulation point superlinearly.