@article{He2022, 
author = {Xiaorui He and Jingyong Tang},
title = {A smooth Levenberg-Marquardt method without nonsingularity condition for wLCP},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {8914-8932},
keywords = {Levenberg-Marquardt method, weighted linear complementarity problem, local error bound condition, sub-quadratic convergence},
url = {https://www.sciopen.com/article/10.3934/math.2022497},
doi = {10.3934/math.2022497},
abstract = {In this paper we consider the weighted Linear Complementarity Problem (wLCP). By using a smooth weighted complementarity function, we reformulate the wLCP as a smooth nonlinear equation and propose a Levenberg-Marquardt method to solve it. The proposed method differentiates itself from the current Levenberg-Marquardt type methods by adopting a simple derivative-free line search technique. It is shown that the proposed method is well-defined and it is globally convergent without requiring wLCP to be monotone. Moreover, the method has local sub-quadratic convergence rate under the local error bound condition which is weaker than the nonsingularity condition. Some numerical results are reported.}
}