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A smoothing Levenberg-Marquardt method for NCP. (English) Zbl 1104.65061
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.

##### MSC:
 65K05 Numerical mathematical programming methods 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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