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 - <p style="text-align: justify;">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.</p>