A Parameter-Self-Adjusting Levenberg-Marquardt Method for Solving Nonsmooth Equations
Year: 2016
Author: Liyan Qi, Xiantao Xiao, Liwei Zhang
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 3 : pp. 317–338
Abstract
A parameter-self-adjusting Levenberg-Marquardt method (PSA-LMM) is proposed for solving a nonlinear system of equations F(x)=0, where F:Rn →Rn is a semismooth mapping. At each iteration, the LM parameter μk is automatically adjusted based on the ratio between actual reduction and predicted reduction. The global convergence of PSA-LMM for solving semismooth equations is demonstrated. Under the BD-regular condition, we prove that PSA-LMM is locally superlinearly convergent for semismooth equations and locally quadratically convergent for strongly semismooth equations. Numerical results for solving nonlinear complementarity problems are presented.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1512-m2015-0333
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 3 : pp. 317–338
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Levenberg-Marquardt method Nonsmooth equations Nonlinear complementarity problems.
Author Details
Liyan Qi Email
Xiantao Xiao Email
Liwei Zhang Email
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