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A Parameter-Self-Adjusting Levenberg-Marquardt Method for Solving Nonsmooth Equations

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:RnRn 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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