Volume 35, Issue 4
Extended Levenberg-Marquardt Method for Composite Function Minimization

Jianchao Huang, Zaiwen Wen & Xiantao Xiao

J. Comp. Math., 35 (2017), pp. 529-546.

Published online: 2017-08

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  • 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.

  • Keywords

Unconstrained minimization Composite function Levenberg-Marquardt method

  • AMS Subject Headings

65K05 90C30 90C53.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

huangjc@sjtu.edu.cn (Jianchao Huang)

wenzw@pku.edu.cn (Zaiwen Wen)

xtxiao@dlut.edu.cn (Xiantao Xiao)

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@Article{JCM-35-529, author = {Huang , Jianchao and Wen , Zaiwen and Xiao , Xiantao }, title = {Extended Levenberg-Marquardt Method for Composite Function Minimization}, journal = {Journal of Computational Mathematics}, year = {2017}, volume = {35}, number = {4}, pages = {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.}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1702-m2016-0699}, url = {http://global-sci.org/intro/article_detail/jcm/10029.html} }
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