On the global convergence of interior-point nonlinear programming algorithms

Detalhes bibliográficos
Autor(a) principal: Haeser,Gabriel
Data de Publicação: 2010
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000200003
Resumo: Carathéodory's lemma states that if we have a linear combination of vectors in <img border=0 src="../../../../img/revistas/cam/v29n2/r_bastao.gif" align=absmiddle>n, we can rewrite this combination using a linearly independent subset. This lemma has been successfully applied in nonlinear optimization in many contexts. In this work we present a new version of this celebrated result, in which we obtained new bounds for the size of the coefficients in the linear combination and we provide examples where these bounds are useful. We show how these new bounds can be used to prove that the internal penalty method converges to KKT points, and we prove that the hypothesis to obtain this result cannot be weakened.The new bounds also provides us some new results of convergence for the quasi feasible interior point ℓ2-penalty method of Chen and Goldfarb [7]. Mathematical subject classification: 90C30, 49K99, 65K05.
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spelling On the global convergence of interior-point nonlinear programming algorithmsnonlinear programmingconstraint qualificationsinterior point methodsCarathéodory's lemma states that if we have a linear combination of vectors in <img border=0 src="../../../../img/revistas/cam/v29n2/r_bastao.gif" align=absmiddle>n, we can rewrite this combination using a linearly independent subset. This lemma has been successfully applied in nonlinear optimization in many contexts. In this work we present a new version of this celebrated result, in which we obtained new bounds for the size of the coefficients in the linear combination and we provide examples where these bounds are useful. We show how these new bounds can be used to prove that the internal penalty method converges to KKT points, and we prove that the hypothesis to obtain this result cannot be weakened.The new bounds also provides us some new results of convergence for the quasi feasible interior point ℓ2-penalty method of Chen and Goldfarb [7]. Mathematical subject classification: 90C30, 49K99, 65K05.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=S1807-03022010000200003Computational &amp; Applied Mathematics v.29 n.2 2010reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022010000200003info:eu-repo/semantics/openAccessHaeser,Gabrieleng2010-09-13T00:00:00Zoai:scielo:S1807-03022010000200003Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2010-09-13T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv On the global convergence of interior-point nonlinear programming algorithms
title On the global convergence of interior-point nonlinear programming algorithms
spellingShingle On the global convergence of interior-point nonlinear programming algorithms
Haeser,Gabriel
nonlinear programming
constraint qualifications
interior point methods
title_short On the global convergence of interior-point nonlinear programming algorithms
title_full On the global convergence of interior-point nonlinear programming algorithms
title_fullStr On the global convergence of interior-point nonlinear programming algorithms
title_full_unstemmed On the global convergence of interior-point nonlinear programming algorithms
title_sort On the global convergence of interior-point nonlinear programming algorithms
author Haeser,Gabriel
author_facet Haeser,Gabriel
author_role author
dc.contributor.author.fl_str_mv Haeser,Gabriel
dc.subject.por.fl_str_mv nonlinear programming
constraint qualifications
interior point methods
topic nonlinear programming
constraint qualifications
interior point methods
description Carathéodory's lemma states that if we have a linear combination of vectors in <img border=0 src="../../../../img/revistas/cam/v29n2/r_bastao.gif" align=absmiddle>n, we can rewrite this combination using a linearly independent subset. This lemma has been successfully applied in nonlinear optimization in many contexts. In this work we present a new version of this celebrated result, in which we obtained new bounds for the size of the coefficients in the linear combination and we provide examples where these bounds are useful. We show how these new bounds can be used to prove that the internal penalty method converges to KKT points, and we prove that the hypothesis to obtain this result cannot be weakened.The new bounds also provides us some new results of convergence for the quasi feasible interior point ℓ2-penalty method of Chen and Goldfarb [7]. Mathematical subject classification: 90C30, 49K99, 65K05.
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=S1807-03022010000200003
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000200003
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S1807-03022010000200003
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 &amp; 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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