Representability of convex sets by analytical linear inequality systems

Autores
Jaume, Daniel Alejandro; Puente, Rubén Oscar
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The solution sets of analytical linear inequality systems posed in the Euclidean space form a transition class between the polyhedral convex sets and the closed convex sets, which are representable by means of linear continuous systems. The constraint systems of many semi-infinite programming problems are analytical, and their feasible sets retain geometric properties of the polyhedral sets which are useful in the numerical treatment of such kind of optimization problems. The Euclidean closed n-dimensional balls admit analytical representation if and only if n<3. This paper solves, in a negative way, the analytical representation problem for a wide class of n-dimensional convex sets, with n⩾3, which includes quasi-polyhedral sets and smooth convex bodies.
Fil: Jaume, Daniel Alejandro. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis; Argentina
Fil: Puente, Rubén Oscar. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina
Materia
ANALYTICAL LINEAR INEQUALITY SYSTEMS
CLOSED CONVEX SETS
CONJUGATE FACESQUASI-POLYHEDRAL SETS
SMOOTH CONVEX BODIES
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:11336/239904
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Representability of convex sets by analytical linear inequality systemsJaume, Daniel AlejandroPuente, Rubén OscarANALYTICAL LINEAR INEQUALITY SYSTEMSCLOSED CONVEX SETSCONJUGATE FACESQUASI-POLYHEDRAL SETSSMOOTH CONVEX BODIEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The solution sets of analytical linear inequality systems posed in the Euclidean space form a transition class between the polyhedral convex sets and the closed convex sets, which are representable by means of linear continuous systems. The constraint systems of many semi-infinite programming problems are analytical, and their feasible sets retain geometric properties of the polyhedral sets which are useful in the numerical treatment of such kind of optimization problems. The Euclidean closed n-dimensional balls admit analytical representation if and only if n<3. This paper solves, in a negative way, the analytical representation problem for a wide class of n-dimensional convex sets, with n⩾3, which includes quasi-polyhedral sets and smooth convex bodies.Fil: Jaume, Daniel Alejandro. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis; ArgentinaFil: Puente, Rubén Oscar. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; ArgentinaElsevier Science Inc.2004-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/239904Jaume, Daniel Alejandro; Puente, Rubén Oscar; Representability of convex sets by analytical linear inequality systems; Elsevier Science Inc.; Linear Algebra and its Applications; 380; 12-2004; 135-1500024-3795CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2003.09.018info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0024379503008103info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:53:27Zoai:ri.conicet.gov.ar:11336/239904instacron: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 09:53:28.068CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Representability of convex sets by analytical linear inequality systems
title Representability of convex sets by analytical linear inequality systems
spellingShingle Representability of convex sets by analytical linear inequality systems
Jaume, Daniel Alejandro
ANALYTICAL LINEAR INEQUALITY SYSTEMS
CLOSED CONVEX SETS
CONJUGATE FACESQUASI-POLYHEDRAL SETS
SMOOTH CONVEX BODIES
title_short Representability of convex sets by analytical linear inequality systems
title_full Representability of convex sets by analytical linear inequality systems
title_fullStr Representability of convex sets by analytical linear inequality systems
title_full_unstemmed Representability of convex sets by analytical linear inequality systems
title_sort Representability of convex sets by analytical linear inequality systems
dc.creator.none.fl_str_mv Jaume, Daniel Alejandro
Puente, Rubén Oscar
author Jaume, Daniel Alejandro
author_facet Jaume, Daniel Alejandro
Puente, Rubén Oscar
author_role author
author2 Puente, Rubén Oscar
author2_role author
dc.subject.none.fl_str_mv ANALYTICAL LINEAR INEQUALITY SYSTEMS
CLOSED CONVEX SETS
CONJUGATE FACESQUASI-POLYHEDRAL SETS
SMOOTH CONVEX BODIES
topic ANALYTICAL LINEAR INEQUALITY SYSTEMS
CLOSED CONVEX SETS
CONJUGATE FACESQUASI-POLYHEDRAL SETS
SMOOTH CONVEX BODIES
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 solution sets of analytical linear inequality systems posed in the Euclidean space form a transition class between the polyhedral convex sets and the closed convex sets, which are representable by means of linear continuous systems. The constraint systems of many semi-infinite programming problems are analytical, and their feasible sets retain geometric properties of the polyhedral sets which are useful in the numerical treatment of such kind of optimization problems. The Euclidean closed n-dimensional balls admit analytical representation if and only if n<3. This paper solves, in a negative way, the analytical representation problem for a wide class of n-dimensional convex sets, with n⩾3, which includes quasi-polyhedral sets and smooth convex bodies.
Fil: Jaume, Daniel Alejandro. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis; Argentina
Fil: Puente, Rubén Oscar. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina
description The solution sets of analytical linear inequality systems posed in the Euclidean space form a transition class between the polyhedral convex sets and the closed convex sets, which are representable by means of linear continuous systems. The constraint systems of many semi-infinite programming problems are analytical, and their feasible sets retain geometric properties of the polyhedral sets which are useful in the numerical treatment of such kind of optimization problems. The Euclidean closed n-dimensional balls admit analytical representation if and only if n<3. This paper solves, in a negative way, the analytical representation problem for a wide class of n-dimensional convex sets, with n⩾3, which includes quasi-polyhedral sets and smooth convex bodies.
publishDate 2004
dc.date.none.fl_str_mv 2004-12
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/11336/239904
Jaume, Daniel Alejandro; Puente, Rubén Oscar; Representability of convex sets by analytical linear inequality systems; Elsevier Science Inc.; Linear Algebra and its Applications; 380; 12-2004; 135-150
0024-3795
CONICET Digital
CONICET
url http://hdl.handle.net/11336/239904
identifier_str_mv Jaume, Daniel Alejandro; Puente, Rubén Oscar; Representability of convex sets by analytical linear inequality systems; Elsevier Science Inc.; Linear Algebra and its Applications; 380; 12-2004; 135-150
0024-3795
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2003.09.018
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0024379503008103
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
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science Inc.
publisher.none.fl_str_mv Elsevier Science Inc.
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
_version_ 1842269226781376512
score 13.13397

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