@Article{JCM-34-3,
author = {Qi, Liyan and Xiao, Xiantao and Zhang, Liwei},
title = {A Parameter-Self-Adjusting Levenberg-Marquardt Method for Solving Nonsmooth Equations},
journal = {Journal of Computational Mathematics},
year = {2016},
volume = {34},
number = {3},
pages = {317--338},
abstract = {<p style="text-align: justify;">A parameter-self-adjusting Levenberg-Marquardt method (PSA-LMM) is proposed for solving a nonlinear system of equations $F(x) = 0$, where $F : \mathbb{R}^n$ →$\mathbb{R}^n$ is a semismooth mapping. At each iteration, the LM parameter $μ_k$ is automatically adjusted based on the ratio between actual reduction and predicted reduction. The global convergence of PSA-LMM for solving semismooth equations is demonstrated. Under the BD-regular condition, we prove that PSA-LMM is locally superlinearly convergent for semismooth equations and locally quadratically convergent for strongly semismooth equations. Numerical results for solving nonlinear complementarity problems are presented.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1512-m2015-0333},
url = {https://global-sci.com/article/84559/a-parameter-self-adjusting-levenberg-marquardt-method-for-solving-nonsmooth-equations}
}