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January  2011, 7(1): 199-210. doi: 10.3934/jimo.2011.7.199

## On the convergence rate of the inexact Levenberg-Marquardt method

 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

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.
Citation: Jinyan Fan, Jianyu Pan. On the convergence rate of the inexact Levenberg-Marquardt method. Journal of Industrial & Management Optimization, 2011, 7 (1) : 199-210. doi: 10.3934/jimo.2011.7.199
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