A Modified Levenberg-Marquardt Method for Nonsmooth Equations with Finitely Many Maximum Functions

A Modified Levenberg-Marquardt Method for Nonsmooth Equations with Finitely Many Maximum Functions

For solving nonsmooth systems of equations, the Levenberg-Marquardt method and its variants are of particular importance because of their locally fast convergent rates. Finitely many maximum functions systems are very useful in the study of nonlinear complementarity problems, variational inequality...

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Main Authors: Shou-qiang Du, Yan Gao
Format: Article
Language:English
Published: Hindawi Limited 2008-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2008/942391
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spelling doaj-56bd63775c3f45c185f8911b590dd6962020-11-24T21:20:18ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472008-01-01200810.1155/2008/942391942391A Modified Levenberg-Marquardt Method for Nonsmooth Equations with Finitely Many Maximum FunctionsShou-qiang Du0Yan Gao1School of Management, University of Shanghai for Science and Technology, Shanghai 200093, ChinaSchool of Management, University of Shanghai for Science and Technology, Shanghai 200093, ChinaFor solving nonsmooth systems of equations, the Levenberg-Marquardt method and its variants are of particular importance because of their locally fast convergent rates. Finitely many maximum functions systems are very useful in the study of nonlinear complementarity problems, variational inequality problems, Karush-Kuhn-Tucker systems of nonlinear programming problems, and many problems in mechanics and engineering. In this paper, we present a modified Levenberg-Marquardt method for nonsmooth equations with finitely many maximum functions. Under mild assumptions, the present method is shown to be convergent Q-linearly. Some numerical results comparing the proposed method with classical reformulations indicate that the modified Levenberg-Marquardt algorithm works quite well in practice.http://dx.doi.org/10.1155/2008/942391
collection DOAJ
language English
format Article
sources DOAJ
author Shou-qiang Du
Yan Gao
spellingShingle Shou-qiang Du
Yan Gao
A Modified Levenberg-Marquardt Method for Nonsmooth Equations with Finitely Many Maximum Functions
Mathematical Problems in Engineering
author_facet Shou-qiang Du
Yan Gao
author_sort Shou-qiang Du
title A Modified Levenberg-Marquardt Method for Nonsmooth Equations with Finitely Many Maximum Functions
title_short A Modified Levenberg-Marquardt Method for Nonsmooth Equations with Finitely Many Maximum Functions
title_full A Modified Levenberg-Marquardt Method for Nonsmooth Equations with Finitely Many Maximum Functions
title_fullStr A Modified Levenberg-Marquardt Method for Nonsmooth Equations with Finitely Many Maximum Functions
title_full_unstemmed A Modified Levenberg-Marquardt Method for Nonsmooth Equations with Finitely Many Maximum Functions
title_sort modified levenberg-marquardt method for nonsmooth equations with finitely many maximum functions
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2008-01-01
description For solving nonsmooth systems of equations, the Levenberg-Marquardt method and its variants are of particular importance because of their locally fast convergent rates. Finitely many maximum functions systems are very useful in the study of nonlinear complementarity problems, variational inequality problems, Karush-Kuhn-Tucker systems of nonlinear programming problems, and many problems in mechanics and engineering. In this paper, we present a modified Levenberg-Marquardt method for nonsmooth equations with finitely many maximum functions. Under mild assumptions, the present method is shown to be convergent Q-linearly. Some numerical results comparing the proposed method with classical reformulations indicate that the modified Levenberg-Marquardt algorithm works quite well in practice.
url http://dx.doi.org/10.1155/2008/942391
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AT shouqiangdu modifiedlevenbergmarquardtmethodfornonsmoothequationswithfinitelymanymaximumfunctions
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