Year: 2017
Author: Jianchao Huang, Zaiwen Wen, Xiantao Xiao
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 4 : pp. 529–546
Abstract
In this paper, we propose an extended Levenberg-Marquardt (ELM) framework that generalizes the classic Levenberg-Marquardt (LM) method to solve the unconstrained minimization problem min $ρ(r(x))$, where $r$ : $\mathbb{R}^n$ → $\mathbb{R}^m$ and $ρ$ : $\mathbb{R}^m$ → $\mathbb{R}$. We also develop a few inexact variants which generalize ELM to the cases where the inner subproblem is not solved exactly and the Jacobian is simplified, or perturbed. Global convergence and local superlinear convergence are established under certain suitable conditions. Numerical results show that our methods are promising.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1702-m2016-0699
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 4 : pp. 529–546
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Unconstrained minimization Composite function Levenberg-Marquardt method.
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