Using truncated conjugate gradient method in trust-region method with two subproblems and backtracking line search

Detalhes bibliográficos
Autor(a) principal: Tang,Mingyun
Data de Publicação: 2010
Outros Autores: Yuan,Ya-Xiang
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000200001
Resumo: A trust-region method with two subproblems and backtracking line search for solving unconstrained optimization is proposed. At every iteration, we use the truncated conjugate gradient method or its variation to solve one of the two subproblems approximately. Backtracking line search is carried out when the trust-region trail step fails. We show that this method have the same convergence properties as the traditional trust-region method based on the truncated conjugate gradient method. Numerical results show that this method is as reliable as the traditional one and more efficient in respect of iterations, CPU time and evaluations. Mathematical subject classification: Primary: 65K05; Secondary: 90C30.
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spelling Using truncated conjugate gradient method in trust-region method with two subproblems and backtracking line searchtruncated conjugate gradienttrust-regiontwo subproblemsbacktrackingconvergenceA trust-region method with two subproblems and backtracking line search for solving unconstrained optimization is proposed. At every iteration, we use the truncated conjugate gradient method or its variation to solve one of the two subproblems approximately. Backtracking line search is carried out when the trust-region trail step fails. We show that this method have the same convergence properties as the traditional trust-region method based on the truncated conjugate gradient method. Numerical results show that this method is as reliable as the traditional one and more efficient in respect of iterations, CPU time and evaluations. Mathematical subject classification: Primary: 65K05; Secondary: 90C30.Sociedade Brasileira de Matemática Aplicada e Computacional2010-06-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000200001Computational & Applied Mathematics v.29 n.2 2010reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022010000200001info:eu-repo/semantics/openAccessTang,MingyunYuan,Ya-Xiangeng2010-07-22T00:00:00Zoai:scielo:S1807-03022010000200001Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2010-07-22T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv Using truncated conjugate gradient method in trust-region method with two subproblems and backtracking line search
title Using truncated conjugate gradient method in trust-region method with two subproblems and backtracking line search
spellingShingle Using truncated conjugate gradient method in trust-region method with two subproblems and backtracking line search
Tang,Mingyun
truncated conjugate gradient
trust-region
two subproblems
backtracking
convergence
title_short Using truncated conjugate gradient method in trust-region method with two subproblems and backtracking line search
title_full Using truncated conjugate gradient method in trust-region method with two subproblems and backtracking line search
title_fullStr Using truncated conjugate gradient method in trust-region method with two subproblems and backtracking line search
title_full_unstemmed Using truncated conjugate gradient method in trust-region method with two subproblems and backtracking line search
title_sort Using truncated conjugate gradient method in trust-region method with two subproblems and backtracking line search
author Tang,Mingyun
author_facet Tang,Mingyun
Yuan,Ya-Xiang
author_role author
author2 Yuan,Ya-Xiang
author2_role author
dc.contributor.author.fl_str_mv Tang,Mingyun
Yuan,Ya-Xiang
dc.subject.por.fl_str_mv truncated conjugate gradient
trust-region
two subproblems
backtracking
convergence
topic truncated conjugate gradient
trust-region
two subproblems
backtracking
convergence
description A trust-region method with two subproblems and backtracking line search for solving unconstrained optimization is proposed. At every iteration, we use the truncated conjugate gradient method or its variation to solve one of the two subproblems approximately. Backtracking line search is carried out when the trust-region trail step fails. We show that this method have the same convergence properties as the traditional trust-region method based on the truncated conjugate gradient method. Numerical results show that this method is as reliable as the traditional one and more efficient in respect of iterations, CPU time and evaluations. Mathematical subject classification: Primary: 65K05; Secondary: 90C30.
publishDate 2010
dc.date.none.fl_str_mv 2010-06-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000200001
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000200001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S1807-03022010000200001
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv Computational & Applied Mathematics v.29 n.2 2010
reponame:Computational & Applied Mathematics
instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron_str SBMAC
institution SBMAC
reponame_str Computational & Applied Mathematics
collection Computational & Applied Mathematics
repository.name.fl_str_mv Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
repository.mail.fl_str_mv ||sbmac@sbmac.org.br
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