On the global convergence   of a parameter-adjusting   Levenberg-Marquardt method

Liyan Qi; Xiantao Xiao; Liwei Zhang

doi:10.3934/naco.2015.5.25

Article Contents

2015, Volume 5, Issue 1: 25-36. Doi: 10.3934/naco.2015.5.25

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On the global convergence of a parameter-adjusting Levenberg-Marquardt method

1.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116023

Received: January 2015

Revised: March 2015

Published: February 2015

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Abstract

The Levenberg-Marquardt (LM) method is a classical but popular method for solving nonlinear equations. Based on the trust region technique, we propose a parameter-adjusting LM (PALM) method, in which the LM parameter $\mu_k$ is self-adjusted at each iteration based on the ratio between actual reduction and predicted reduction. Under the level-bounded condition, we prove the global convergence of PALM. We also propose a modified parameter-adjusting LM (MPALM) method. Numerical results show that the two methods are very efficient.

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Mathematics Subject Classification: Primary: 90C30, 65K05.

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