On the convergence rate of the inexact Levenberg-Marquardt method

Jinyan Fan; Jianyu Pan

doi:10.3934/jimo.2011.7.199

Article Contents

2011, Volume 7, Issue 1: 199-210. Doi: 10.3934/jimo.2011.7.199

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On the convergence rate of the inexact Levenberg-Marquardt method

Jinyan Fan^1, and
Jianyu Pan^2,

1.
Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240
2.
Department of Mathematics, East China Normal University, Shanghai 200062

Received: July 2010

Revised: November 2010

Published: January 2011

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Abstract

In this paper we study the convergence rate of the inexact Levenberg-Marquardt method for nonlinear equations. Under the local error bound condition which is weaker than nonsingularity, we derive an explicit formula of the convergence order of the inexact LM method, which is a continuous function with respect to not only the LM parameter but also the perturbation vector. The new formula includes many convergence rate results in the literature as its special cases.

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Mathematics Subject Classification: 90C30, 65K05, 34A34.

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References

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