The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems

Autores
Birgin, Ernesto G.; Fernández Ferreyra, Damián Roberto; Martínez, J. M.
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented.
Fil: Birgin, Ernesto G.. Universidade de Sao Paulo; Brasil
Fil: Fernández Ferreyra, Damián Roberto. Universidade Estadual de Campinas; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Martínez, J. M.. Universidade Estadual de Campinas; Brasil
Materia
Augmented Lagrangian Methods
Nonlinear Programming
Numerical Experiments
Penalty Parameters
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/81242
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/81242
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblemsBirgin, Ernesto G.Fernández Ferreyra, Damián RobertoMartínez, J. M.Augmented Lagrangian MethodsNonlinear ProgrammingNumerical ExperimentsPenalty Parametershttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented.Fil: Birgin, Ernesto G.. Universidade de Sao Paulo; BrasilFil: Fernández Ferreyra, Damián Roberto. Universidade Estadual de Campinas; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Martínez, J. M.. Universidade Estadual de Campinas; BrasilTaylor & Francis Ltd2012-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/81242Birgin, Ernesto G.; Fernández Ferreyra, Damián Roberto; Martínez, J. M.; The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems; Taylor & Francis Ltd; Optimization Methods And Software; 27; 6; 12-2012; 1001-10241055-67881029-4937CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1080/10556788.2011.556634info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/abs/10.1080/10556788.2011.556634info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:52:09Zoai:ri.conicet.gov.ar:11336/81242instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:52:09.794CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems
title The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems
spellingShingle The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems
Birgin, Ernesto G.
Augmented Lagrangian Methods
Nonlinear Programming
Numerical Experiments
Penalty Parameters
title_short The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems
title_full The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems
title_fullStr The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems
title_full_unstemmed The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems
title_sort The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems
dc.creator.none.fl_str_mv Birgin, Ernesto G.
Fernández Ferreyra, Damián Roberto
Martínez, J. M.
author Birgin, Ernesto G.
author_facet Birgin, Ernesto G.
Fernández Ferreyra, Damián Roberto
Martínez, J. M.
author_role author
author2 Fernández Ferreyra, Damián Roberto
Martínez, J. M.
author2_role author
author
dc.subject.none.fl_str_mv Augmented Lagrangian Methods
Nonlinear Programming
Numerical Experiments
Penalty Parameters
topic Augmented Lagrangian Methods
Nonlinear Programming
Numerical Experiments
Penalty Parameters
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented.
Fil: Birgin, Ernesto G.. Universidade de Sao Paulo; Brasil
Fil: Fernández Ferreyra, Damián Roberto. Universidade Estadual de Campinas; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Martínez, J. M.. Universidade Estadual de Campinas; Brasil
description Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented.
publishDate 2012
dc.date.none.fl_str_mv 2012-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/81242
Birgin, Ernesto G.; Fernández Ferreyra, Damián Roberto; Martínez, J. M.; The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems; Taylor & Francis Ltd; Optimization Methods And Software; 27; 6; 12-2012; 1001-1024
1055-6788
1029-4937
CONICET Digital
CONICET
url http://hdl.handle.net/11336/81242
identifier_str_mv Birgin, Ernesto G.; Fernández Ferreyra, Damián Roberto; Martínez, J. M.; The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems; Taylor & Francis Ltd; Optimization Methods And Software; 27; 6; 12-2012; 1001-1024
1055-6788
1029-4937
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1080/10556788.2011.556634
info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/abs/10.1080/10556788.2011.556634
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis Ltd
publisher.none.fl_str_mv Taylor & Francis Ltd
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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