A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations

In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented metho...

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Detalles Bibliográficos
Autores principales: Li, Yong, Yuan, Gonglin, Wei, Zengxin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2015
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4423997/
https://www.ncbi.nlm.nih.gov/pubmed/25950725
http://dx.doi.org/10.1371/journal.pone.0120993
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author Li, Yong
Yuan, Gonglin
Wei, Zengxin
author_facet Li, Yong
Yuan, Gonglin
Wei, Zengxin
author_sort Li, Yong
collection PubMed
description In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented method is established under suitable conditions. The numerical results of the test problems show that the method is competitive with the norm method.
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spelling pubmed-44239972015-05-13 A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations Li, Yong Yuan, Gonglin Wei, Zengxin PLoS One Research Article In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented method is established under suitable conditions. The numerical results of the test problems show that the method is competitive with the norm method. Public Library of Science 2015-05-07 /pmc/articles/PMC4423997/ /pubmed/25950725 http://dx.doi.org/10.1371/journal.pone.0120993 Text en © 2015 Li et al http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
spellingShingle Research Article
Li, Yong
Yuan, Gonglin
Wei, Zengxin
A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations
title A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations
title_full A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations
title_fullStr A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations
title_full_unstemmed A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations
title_short A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations
title_sort limited-memory bfgs algorithm based on a trust-region quadratic model for large-scale nonlinear equations
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4423997/
https://www.ncbi.nlm.nih.gov/pubmed/25950725
http://dx.doi.org/10.1371/journal.pone.0120993
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