TY - JOUR
T1 - Extended Levenberg-Marquardt Method for Composite Function Minimization
AU - Huang , Jianchao
AU - Wen , Zaiwen
AU - Xiao , Xiantao
JO - Journal of Computational Mathematics
VL - 4
SP - 529
EP - 546
PY - 2017
DA - 2017/08
SN - 35
DO - http://doi.org/10.4208/jcm.1702-m2016-0699
UR - https://global-sci.org/intro/article_detail/jcm/10029.html
KW - Unconstrained minimization, Composite function, Levenberg-Marquardt method.
AB - <p style="text-align: justify;">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.</p>