A smoothing Levenberg-Marquardt method for NCP (Q2507812)

Nonlinear complementarity problems (NCPs) are converted to an equivalent system of smooth nonlinear equations by using a smoothing technique. Then a Levenberg-Marquardt type method is used to solve the system of nonlinear equations. The method has the following merits: (i) any cluster point of the iteration sequence is a solution of the \(P_{0}\)-NCP; (ii) it generates a bounded sequence if the \(P_{0}\)-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 \(P_{0}\)-NCP superlinearly; (iv) for the \(P_{0}\)-NCP, if an accumulation point of the iteration sequence satisfies strict complementary condition, then the whole sequence converges to this accumulation point superlinearly.