A smoothing Levenberg–Marquardt method for NCP

摘要

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.