A note on the McCormick second-order constraint qualification

Autores
Fazzio, Nadia Soledad; Sanchez, María Daniela; Schuverdt, María Laura
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The study of optimality conditions and constraint qualification is a key  topic in nonlinear optimization. In this work, we present a reformulation of the well-known second-order constraint qualification described by McCormick in [17]. This reformulation is based on the use of feasible arcs, but is independent of Lagrange multipliers. Using such a reformulation, we can show that a local minimizer verifies the strong second-order necessary optimality condition. We can also prove that the reformulation is weaker than the known relaxed constant rank constraint qualification in [19]. Furthermore, we demonstrate that the condition is neither related to the MFCQ+WCR in [8] nor to the CCP2 condition, the companion constraint qualification associated with the second-order sequential optimality condition AKKT2 in [5].
Fil: Fazzio, Nadia Soledad. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Sanchez, María Daniela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Schuverdt, María Laura. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Materia
NONLINEAR PROGRAMMING
SECOND-ORDER OPTIMALITY CONDITIONS
CONSTRAINT QUALIFICATION
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:11336/221422
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A note on the McCormick second-order constraint qualificationFazzio, Nadia SoledadSanchez, María DanielaSchuverdt, María LauraNONLINEAR PROGRAMMINGSECOND-ORDER OPTIMALITY CONDITIONSCONSTRAINT QUALIFICATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The study of optimality conditions and constraint qualification is a key  topic in nonlinear optimization. In this work, we present a reformulation of the well-known second-order constraint qualification described by McCormick in [17]. This reformulation is based on the use of feasible arcs, but is independent of Lagrange multipliers. Using such a reformulation, we can show that a local minimizer verifies the strong second-order necessary optimality condition. We can also prove that the reformulation is weaker than the known relaxed constant rank constraint qualification in [19]. Furthermore, we demonstrate that the condition is neither related to the MFCQ+WCR in [8] nor to the CCP2 condition, the companion constraint qualification associated with the second-order sequential optimality condition AKKT2 in [5].Fil: Fazzio, Nadia Soledad. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: Sanchez, María Daniela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: Schuverdt, María Laura. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaBrazilian Society of Applied and Computational Mathematics2022-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/221422Fazzio, Nadia Soledad; Sanchez, María Daniela; Schuverdt, María Laura; A note on the McCormick second-order constraint qualification; Brazilian Society of Applied and Computational Mathematics; Trends in Computational and Applied Mathematics; 23; 4; 12-2022; 769-7812676-0029CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://tema.sbmac.org.br/tema/article/download/1625/1141info:eu-repo/semantics/altIdentifier/doi/10.5540/tcam.2022.023.04.00769info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:44:38Zoai:ri.conicet.gov.ar:11336/221422instacron: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 09:44:38.555CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A note on the McCormick second-order constraint qualification
title A note on the McCormick second-order constraint qualification
spellingShingle A note on the McCormick second-order constraint qualification
Fazzio, Nadia Soledad
NONLINEAR PROGRAMMING
SECOND-ORDER OPTIMALITY CONDITIONS
CONSTRAINT QUALIFICATION
title_short A note on the McCormick second-order constraint qualification
title_full A note on the McCormick second-order constraint qualification
title_fullStr A note on the McCormick second-order constraint qualification
title_full_unstemmed A note on the McCormick second-order constraint qualification
title_sort A note on the McCormick second-order constraint qualification
dc.creator.none.fl_str_mv Fazzio, Nadia Soledad
Sanchez, María Daniela
Schuverdt, María Laura
author Fazzio, Nadia Soledad
author_facet Fazzio, Nadia Soledad
Sanchez, María Daniela
Schuverdt, María Laura
author_role author
author2 Sanchez, María Daniela
Schuverdt, María Laura
author2_role author
author
dc.subject.none.fl_str_mv NONLINEAR PROGRAMMING
SECOND-ORDER OPTIMALITY CONDITIONS
CONSTRAINT QUALIFICATION
topic NONLINEAR PROGRAMMING
SECOND-ORDER OPTIMALITY CONDITIONS
CONSTRAINT QUALIFICATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The study of optimality conditions and constraint qualification is a key  topic in nonlinear optimization. In this work, we present a reformulation of the well-known second-order constraint qualification described by McCormick in [17]. This reformulation is based on the use of feasible arcs, but is independent of Lagrange multipliers. Using such a reformulation, we can show that a local minimizer verifies the strong second-order necessary optimality condition. We can also prove that the reformulation is weaker than the known relaxed constant rank constraint qualification in [19]. Furthermore, we demonstrate that the condition is neither related to the MFCQ+WCR in [8] nor to the CCP2 condition, the companion constraint qualification associated with the second-order sequential optimality condition AKKT2 in [5].
Fil: Fazzio, Nadia Soledad. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Sanchez, María Daniela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Schuverdt, María Laura. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
description The study of optimality conditions and constraint qualification is a key  topic in nonlinear optimization. In this work, we present a reformulation of the well-known second-order constraint qualification described by McCormick in [17]. This reformulation is based on the use of feasible arcs, but is independent of Lagrange multipliers. Using such a reformulation, we can show that a local minimizer verifies the strong second-order necessary optimality condition. We can also prove that the reformulation is weaker than the known relaxed constant rank constraint qualification in [19]. Furthermore, we demonstrate that the condition is neither related to the MFCQ+WCR in [8] nor to the CCP2 condition, the companion constraint qualification associated with the second-order sequential optimality condition AKKT2 in [5].
publishDate 2022
dc.date.none.fl_str_mv 2022-12
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/11336/221422
Fazzio, Nadia Soledad; Sanchez, María Daniela; Schuverdt, María Laura; A note on the McCormick second-order constraint qualification; Brazilian Society of Applied and Computational Mathematics; Trends in Computational and Applied Mathematics; 23; 4; 12-2022; 769-781
2676-0029
CONICET Digital
CONICET
url http://hdl.handle.net/11336/221422
identifier_str_mv Fazzio, Nadia Soledad; Sanchez, María Daniela; Schuverdt, María Laura; A note on the McCormick second-order constraint qualification; Brazilian Society of Applied and Computational Mathematics; Trends in Computational and Applied Mathematics; 23; 4; 12-2022; 769-781
2676-0029
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://tema.sbmac.org.br/tema/article/download/1625/1141
info:eu-repo/semantics/altIdentifier/doi/10.5540/tcam.2022.023.04.00769
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
application/pdf
dc.publisher.none.fl_str_mv Brazilian Society of Applied and Computational Mathematics
publisher.none.fl_str_mv Brazilian Society of Applied and Computational Mathematics
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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