On the divergence of line search methods

Detalhes bibliográficos
Autor(a) principal: Mascarenhas,Walter F.
Data de Publicação: 2007
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022007000100006
Resumo: We discuss the convergence of line search methods for minimization. We explain how Newton's method and the BFGS method can fail even if the restrictions of the objective function to the search lines are strictly convex functions, the level sets of the objective functions are compact, the line searches are exact and the Wolfe conditions are satisfied. This explanation illustrates a new way to combine general mathematical concepts and symbolic computation to analyze the convergence of line search methods. It also illustrate the limitations of the asymptotic analysis of the iterates of nonlinear programming algorithms.
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spelling On the divergence of line search methodsline search methodsconvergenceWe discuss the convergence of line search methods for minimization. We explain how Newton's method and the BFGS method can fail even if the restrictions of the objective function to the search lines are strictly convex functions, the level sets of the objective functions are compact, the line searches are exact and the Wolfe conditions are satisfied. This explanation illustrates a new way to combine general mathematical concepts and symbolic computation to analyze the convergence of line search methods. It also illustrate the limitations of the asymptotic analysis of the iterates of nonlinear programming algorithms.Sociedade Brasileira de Matemática Aplicada e Computacional2007-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022007000100006Computational & Applied Mathematics v.26 n.1 2007reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMACinfo:eu-repo/semantics/openAccessMascarenhas,Walter F.eng2007-05-10T00:00:00Zoai:scielo:S1807-03022007000100006Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2007-05-10T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv On the divergence of line search methods
title On the divergence of line search methods
spellingShingle On the divergence of line search methods
Mascarenhas,Walter F.
line search methods
convergence
title_short On the divergence of line search methods
title_full On the divergence of line search methods
title_fullStr On the divergence of line search methods
title_full_unstemmed On the divergence of line search methods
title_sort On the divergence of line search methods
author Mascarenhas,Walter F.
author_facet Mascarenhas,Walter F.
author_role author
dc.contributor.author.fl_str_mv Mascarenhas,Walter F.
dc.subject.por.fl_str_mv line search methods
convergence
topic line search methods
convergence
description We discuss the convergence of line search methods for minimization. We explain how Newton's method and the BFGS method can fail even if the restrictions of the objective function to the search lines are strictly convex functions, the level sets of the objective functions are compact, the line searches are exact and the Wolfe conditions are satisfied. This explanation illustrates a new way to combine general mathematical concepts and symbolic computation to analyze the convergence of line search methods. It also illustrate the limitations of the asymptotic analysis of the iterates of nonlinear programming algorithms.
publishDate 2007
dc.date.none.fl_str_mv 2007-01-01
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=S1807-03022007000100006
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022007000100006
dc.language.iso.fl_str_mv eng
language eng
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.26 n.1 2007
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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