TWO NEW WEAK CONSTRAINT QUALIFICATIONS and APPLICATIONS

We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major o...

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Detalhes bibliográficos
Autores: Andreani, Roberto, Haeser, Gabriel [UNIFESP], Laura Schuverdt, Maria, Silva, Paulo J. S.
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2012
País:Brasil
Recursos:Universidade Federal de São Paulo (UNIFESP)
Repositório:Repositório Institucional da UNIFESP
Idioma:inglês
OAI Identifier:oai:repositorio.unifesp.br:11600/34361
Acesso em linha:http://dx.doi.org/10.1137/110843939
http://repositorio.unifesp.br/handle/11600/34361
Access Level:Acceso aberto
Palavra-chave:constraint qualifications
error bound
algorithmic convergence
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spelling TWO NEW WEAK CONSTRAINT QUALIFICATIONS and APPLICATIONSconstraint qualificationserror boundalgorithmic convergenceWe present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a CQ. This is done in the first new CQ, which we call the constant rank of the subspace component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, such as local stability and the validity of an error bound. We also introduce an even weaker CQ, called the constant positive generator (CPG), which can replace RCPLD in the analysis of the global convergence of algorithms. We close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: sequential quadratic programming, augmented Lagrangians, interior point algorithms, and inexact restoration.Univ Estadual Campinas, Dept Appl Math, Inst Math Stat & Sci Comp, Campinas, SP, BrazilUniversidade Federal de São Paulo, Inst Sci & Technol, Sao Jose Dos Campos, SP, BrazilNatl Univ La Plata, FCE, Dept Math, CONICET, RA-1900 La Plata, Bs As, ArgentinaUniv São Paulo, Inst Math & Stat, São Paulo, BrazilUniversidade Federal de São Paulo, Inst Sci & Technol, Sao Jose Dos Campos, SP, BrazilWeb of ScienceConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CNPq: E-26/171.510/2006-APQ1FAPESP: 2006/53768-0FAPESP: 2009/09414-7FAPESP: 2010/19720-5CNPq: 300900/2009-0CNPq: 303030/2007-0CNPq: 305740/2010-5CNPq: 474138/2008-9Siam PublicationsUniversidade Estadual de Campinas (UNICAMP)Universidade Federal de São Paulo (UNIFESP)Natl Univ La PlataUniversidade de São Paulo (USP)2016-01-24T14:17:36Z2016-01-24T14:17:36Z2012-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion1109-1135application/pdfhttp://dx.doi.org/10.1137/110843939Siam Journal On Optimization. Philadelphia: Siam Publications, v. 22, n. 3, p. 1109-1135, 2012.10.1137/110843939WOS000310214800019.pdf1052-6234http://repositorio.unifesp.br/handle/11600/34361WOS:000310214800019ark:/48912/001300002khqpengSiam Journal On Optimizationinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UNIFESPinstname:Universidade Federal de São Paulo (UNIFESP)instacron:UNIFESPAndreani, RobertoHaeser, Gabriel [UNIFESP]Laura Schuverdt, MariaSilva, Paulo J. S.2024-08-08T09:56:52Zoai:repositorio.unifesp.br:11600/34361Repositório InstitucionalPUBhttp://www.repositorio.unifesp.br/oai/requestbiblioteca.csp@unifesp.bropendoar:34652024-08-08T09:56:52Repositório Institucional da UNIFESP - Universidade Federal de São Paulo (UNIFESP)false
dc.title.none.fl_str_mv TWO NEW WEAK CONSTRAINT QUALIFICATIONS and APPLICATIONS
title TWO NEW WEAK CONSTRAINT QUALIFICATIONS and APPLICATIONS
spellingShingle TWO NEW WEAK CONSTRAINT QUALIFICATIONS and APPLICATIONS
Andreani, Roberto
constraint qualifications
error bound
algorithmic convergence
title_short TWO NEW WEAK CONSTRAINT QUALIFICATIONS and APPLICATIONS
title_full TWO NEW WEAK CONSTRAINT QUALIFICATIONS and APPLICATIONS
title_fullStr TWO NEW WEAK CONSTRAINT QUALIFICATIONS and APPLICATIONS
title_full_unstemmed TWO NEW WEAK CONSTRAINT QUALIFICATIONS and APPLICATIONS
title_sort TWO NEW WEAK CONSTRAINT QUALIFICATIONS and APPLICATIONS
dc.creator.none.fl_str_mv Andreani, Roberto
Haeser, Gabriel [UNIFESP]
Laura Schuverdt, Maria
Silva, Paulo J. S.
author Andreani, Roberto
author_facet Andreani, Roberto
Haeser, Gabriel [UNIFESP]
Laura Schuverdt, Maria
Silva, Paulo J. S.
author_role author
author2 Haeser, Gabriel [UNIFESP]
Laura Schuverdt, Maria
Silva, Paulo J. S.
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade Estadual de Campinas (UNICAMP)
Universidade Federal de São Paulo (UNIFESP)
Natl Univ La Plata
Universidade de São Paulo (USP)
dc.subject.por.fl_str_mv constraint qualifications
error bound
algorithmic convergence
topic constraint qualifications
error bound
algorithmic convergence
description We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a CQ. This is done in the first new CQ, which we call the constant rank of the subspace component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, such as local stability and the validity of an error bound. We also introduce an even weaker CQ, called the constant positive generator (CPG), which can replace RCPLD in the analysis of the global convergence of algorithms. We close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: sequential quadratic programming, augmented Lagrangians, interior point algorithms, and inexact restoration.
publishDate 2012
dc.date.none.fl_str_mv 2012-01-01
2016-01-24T14:17:36Z
2016-01-24T14:17:36Z
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://dx.doi.org/10.1137/110843939
Siam Journal On Optimization. Philadelphia: Siam Publications, v. 22, n. 3, p. 1109-1135, 2012.
10.1137/110843939
WOS000310214800019.pdf
1052-6234
http://repositorio.unifesp.br/handle/11600/34361
WOS:000310214800019
dc.identifier.dark.fl_str_mv ark:/48912/001300002khqp
url http://dx.doi.org/10.1137/110843939
http://repositorio.unifesp.br/handle/11600/34361
identifier_str_mv Siam Journal On Optimization. Philadelphia: Siam Publications, v. 22, n. 3, p. 1109-1135, 2012.
10.1137/110843939
WOS000310214800019.pdf
1052-6234
WOS:000310214800019
ark:/48912/001300002khqp
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Siam Journal On Optimization
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 1109-1135
application/pdf
dc.publisher.none.fl_str_mv Siam Publications
publisher.none.fl_str_mv Siam Publications
dc.source.none.fl_str_mv reponame:Repositório Institucional da UNIFESP
instname:Universidade Federal de São Paulo (UNIFESP)
instacron:UNIFESP
instname_str Universidade Federal de São Paulo (UNIFESP)
instacron_str UNIFESP
institution UNIFESP
reponame_str Repositório Institucional da UNIFESP
collection Repositório Institucional da UNIFESP
repository.name.fl_str_mv Repositório Institucional da UNIFESP - Universidade Federal de São Paulo (UNIFESP)
repository.mail.fl_str_mv biblioteca.csp@unifesp.br
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score 15.301629

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