# American Institute of Mathematical Sciences

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2015, 5(1): 25-36. doi: 10.3934/naco.2015.5.25

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

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

Received  January 2015 Revised  March 2015 Published  March 2015

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.
Citation: Liyan Qi, Xiantao Xiao, Liwei Zhang. On the global convergence of a parameter-adjusting Levenberg-Marquardt method. Numerical Algebra, Control & Optimization, 2015, 5 (1) : 25-36. doi: 10.3934/naco.2015.5.25
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