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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.

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