Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions

Autores
Fernández Ferreyra, Damián Roberto
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
It is well-known that the primal quadratic growth condition of the classical augmented Lagrangian around a local minimizer can be obtained under the second-order sufficient optimality condition. In this paper, we show that those conditions are indeed equivalent. Moreover, we prove that the primal quadratic growth condition of the sharp augmented Lagrangian around a local minimizer is in fact equivalent to the weak second-order sufficient optimality condition. In addition, we present some secondary results involving the sharp augmented Lagrangian.
Fil: Fernández Ferreyra, Damián Roberto. 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. Universidad Nacional de Córdoba; Argentina
Materia
AUGMENTED LAGRANGIAN
SECOND-ORDER SUFFICIENT OPTIMALITY CONDITION
SHARP AUGMENTED LAGRANGIAN
WEAK SECOND-ORDER SUFFICIENT OPTIMALITY CONDITION
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:11336/143331
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/143331
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Augmented Lagrangians quadratic growth and second-order sufficient optimality conditionsFernández Ferreyra, Damián RobertoAUGMENTED LAGRANGIANSECOND-ORDER SUFFICIENT OPTIMALITY CONDITIONSHARP AUGMENTED LAGRANGIANWEAK SECOND-ORDER SUFFICIENT OPTIMALITY CONDITIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1It is well-known that the primal quadratic growth condition of the classical augmented Lagrangian around a local minimizer can be obtained under the second-order sufficient optimality condition. In this paper, we show that those conditions are indeed equivalent. Moreover, we prove that the primal quadratic growth condition of the sharp augmented Lagrangian around a local minimizer is in fact equivalent to the weak second-order sufficient optimality condition. In addition, we present some secondary results involving the sharp augmented Lagrangian.Fil: Fernández Ferreyra, Damián Roberto. 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. Universidad Nacional de Córdoba; ArgentinaTaylor & Francis Ltd2020-08-21info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/143331Fernández Ferreyra, Damián Roberto; Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions; Taylor & Francis Ltd; Optimization; 21-8-2020; 1-170233-19341029-4945CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1080/02331934.2020.1804567info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/full/10.1080/02331934.2020.1804567info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:15:46Zoai:ri.conicet.gov.ar:11336/143331instacron: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:34982025-11-05 10:15:46.718CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions
title Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions
spellingShingle Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions
Fernández Ferreyra, Damián Roberto
AUGMENTED LAGRANGIAN
SECOND-ORDER SUFFICIENT OPTIMALITY CONDITION
SHARP AUGMENTED LAGRANGIAN
WEAK SECOND-ORDER SUFFICIENT OPTIMALITY CONDITION
title_short Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions
title_full Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions
title_fullStr Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions
title_full_unstemmed Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions
title_sort Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions
dc.creator.none.fl_str_mv Fernández Ferreyra, Damián Roberto
author Fernández Ferreyra, Damián Roberto
author_facet Fernández Ferreyra, Damián Roberto
author_role author
dc.subject.none.fl_str_mv AUGMENTED LAGRANGIAN
SECOND-ORDER SUFFICIENT OPTIMALITY CONDITION
SHARP AUGMENTED LAGRANGIAN
WEAK SECOND-ORDER SUFFICIENT OPTIMALITY CONDITION
topic AUGMENTED LAGRANGIAN
SECOND-ORDER SUFFICIENT OPTIMALITY CONDITION
SHARP AUGMENTED LAGRANGIAN
WEAK SECOND-ORDER SUFFICIENT OPTIMALITY CONDITION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv It is well-known that the primal quadratic growth condition of the classical augmented Lagrangian around a local minimizer can be obtained under the second-order sufficient optimality condition. In this paper, we show that those conditions are indeed equivalent. Moreover, we prove that the primal quadratic growth condition of the sharp augmented Lagrangian around a local minimizer is in fact equivalent to the weak second-order sufficient optimality condition. In addition, we present some secondary results involving the sharp augmented Lagrangian.
Fil: Fernández Ferreyra, Damián Roberto. 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. Universidad Nacional de Córdoba; Argentina
description It is well-known that the primal quadratic growth condition of the classical augmented Lagrangian around a local minimizer can be obtained under the second-order sufficient optimality condition. In this paper, we show that those conditions are indeed equivalent. Moreover, we prove that the primal quadratic growth condition of the sharp augmented Lagrangian around a local minimizer is in fact equivalent to the weak second-order sufficient optimality condition. In addition, we present some secondary results involving the sharp augmented Lagrangian.
publishDate 2020
dc.date.none.fl_str_mv 2020-08-21
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/11336/143331
Fernández Ferreyra, Damián Roberto; Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions; Taylor & Francis Ltd; Optimization; 21-8-2020; 1-17
0233-1934
1029-4945
CONICET Digital
CONICET
url http://hdl.handle.net/11336/143331
identifier_str_mv Fernández Ferreyra, Damián Roberto; Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions; Taylor & Francis Ltd; Optimization; 21-8-2020; 1-17
0233-1934
1029-4945
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1080/02331934.2020.1804567
info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/full/10.1080/02331934.2020.1804567
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 13.087074

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