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Volume 22, Issue 5
A Smoothing Levenberg-Marquardt Type Method for LCP

Juliang Zhang & Jian Chen

J. Comp. Math., 22 (2004), pp. 735-752.

Published online: 2004-10

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  • Abstract

In this paper, we convert the linear complementarity problem to a system of semismooth nonlinear equations by using smoothing technique. Then we use Levenberg-Marquardt type method to solve this system. Taking advantage of the new results obtained by Dan, Yamashita and Fukushima [11, 33], the global and local superlinear convergence properties of the method are obtained under very mild conditions. Especially, the algorithm is locally superlinearly convergent under the assumption of either strict complementarity or certain nonsingularity. Preliminary numerical experiments are reported to show the efficiency of the algorithm.

  • Keywords

LCP, Levenberg-Marquardt method, Smoothing technique, $P_0$ matrix, Superlinear convergence.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-735, author = {Zhang , Juliang and Chen , Jian}, title = {A Smoothing Levenberg-Marquardt Type Method for LCP}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {5}, pages = {735--752}, abstract = {

In this paper, we convert the linear complementarity problem to a system of semismooth nonlinear equations by using smoothing technique. Then we use Levenberg-Marquardt type method to solve this system. Taking advantage of the new results obtained by Dan, Yamashita and Fukushima [11, 33], the global and local superlinear convergence properties of the method are obtained under very mild conditions. Especially, the algorithm is locally superlinearly convergent under the assumption of either strict complementarity or certain nonsingularity. Preliminary numerical experiments are reported to show the efficiency of the algorithm.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10300.html} }
TY - JOUR T1 - A Smoothing Levenberg-Marquardt Type Method for LCP AU - Zhang , Juliang AU - Chen , Jian JO - Journal of Computational Mathematics VL - 5 SP - 735 EP - 752 PY - 2004 DA - 2004/10 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10300.html KW - LCP, Levenberg-Marquardt method, Smoothing technique, $P_0$ matrix, Superlinear convergence. AB -

In this paper, we convert the linear complementarity problem to a system of semismooth nonlinear equations by using smoothing technique. Then we use Levenberg-Marquardt type method to solve this system. Taking advantage of the new results obtained by Dan, Yamashita and Fukushima [11, 33], the global and local superlinear convergence properties of the method are obtained under very mild conditions. Especially, the algorithm is locally superlinearly convergent under the assumption of either strict complementarity or certain nonsingularity. Preliminary numerical experiments are reported to show the efficiency of the algorithm.

Zhang , Juliang and Chen , Jian. (2004). A Smoothing Levenberg-Marquardt Type Method for LCP. Journal of Computational Mathematics. 22 (5). 735-752. doi:
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