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

Ju-liang Zhang & Jian Chen

DOI:

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 Po matrix Superlinear convergence

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@Article{JCM-22-735, author = {}, 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 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 KW - Levenberg-Marquardt method KW - Smoothing technique KW - Po matrix KW - 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.
Ju-liang Zhang & Jian Chen. (1970). A Smoothing Levenberg-Marquardt Type Method for LCP. Journal of Computational Mathematics. 22 (5). 735-752. doi:
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