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Research articles

ScienceAsia 43(2017): 377-382 |doi: 10.2306/scienceasia1513-1874.2017.43.377


On the local convergence of a Levenberg-Marquardt method for nonsmooth nonlinear complementarity problems


Linsen Songa,b,*, Yan Gaoa

 
ABSTRACT:     This paper is concerned with a nonlinear complementarity problem, the related functions of which are locally Lipschitzian. As is well known, the nonlinear complementarity problem is reformulated as a system of nonsmooth equations based on complementarity functions, and Levenberg-Marquardt methods are often used to solve it. However, an element of the nonlinear complementarity functions' B-differential is required in these methods, which is always difficult or time consuming to obtain for a locally Lipschitzian function. By introducing a new subdifferential, rather than the B-differential of the nonlinear complementarity function, a modified Levenberg-Marquardt method is presented, and the local behaviour of this method under the local error bound condition, which is less strong than nonsingular, is shown. Finally, the numerical tests illustrate the effectiveness of the given algorithm.

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a School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China
b School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China

* Corresponding author, E-mail: slinsen@163.com

Received 14 Jul 2017, Accepted 15 Nov 2017