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Zbl 1104.65061
Zhang, Ju-Liang; Zhang, Xiangsun
A smoothing Levenberg-Marquardt method for NCP. (English)
[J] Appl. Math. Comput. 178, No. 2, 212-228 (2006). ISSN 0096-3003

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 2000:: *65K05 Mathematical programming (numerical methods)
90C33 Complementarity problems

Keywords: Levenberg-Marquardt method; smoothing technique; $P_{0}$ matrix; superlinear convergence; nonlinear complementarity problems

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