Conjugacy for closed convex sets

Autores
Jaume, Daniel Alejandro; Puente, Rubén Oscar
Año de publicación
2005
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Even though the polarity is a well defined operation for arbitrary subsets in the Euclidean n-dimensional space, the related operation of conjugacy of faces appears defined in the literature exclusively for either convex bodies containning the origin as interior point and their polar sets, or for closed convex cones. This paper extends the geometry of closed convex cones and convex bodies to unbounded convex sets (and, in a dual way, to those closed convex sets containing the origin at the boundary), not only for the sake of theoretical completeness, but also for the potential applications of this theory in the fields of Convex Programming and Semi-infinite Programming. Introducing the recession cone into the analysis we develop a general theory of conjugacy which, together with the new concept of curvature index of a convex set on a face, allows us to establish a strong result on complementary dimensions of conjugate faces which extends a well-known result on polytopes.
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
CONJUGACY
CLOSED
CONVEX
SETS
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:11336/240594
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Conjugacy for closed convex setsJaume, Daniel AlejandroPuente, Rubén OscarCONJUGACYCLOSEDCONVEXSETShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Even though the polarity is a well defined operation for arbitrary subsets in the Euclidean n-dimensional space, the related operation of conjugacy of faces appears defined in the literature exclusively for either convex bodies containning the origin as interior point and their polar sets, or for closed convex cones. This paper extends the geometry of closed convex cones and convex bodies to unbounded convex sets (and, in a dual way, to those closed convex sets containing the origin at the boundary), not only for the sake of theoretical completeness, but also for the potential applications of this theory in the fields of Convex Programming and Semi-infinite Programming. Introducing the recession cone into the analysis we develop a general theory of conjugacy which, together with the new concept of curvature index of a convex set on a face, allows us to establish a strong result on complementary dimensions of conjugate faces which extends a well-known result on polytopes.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; ArgentinaHedelmann Verlag2005-12info: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/11336/240594Jaume, Daniel Alejandro; Puente, Rubén Oscar; Conjugacy for closed convex sets; Hedelmann Verlag; Beitrage R Algebra Geom; 46; 1; 12-2005; 131-1490138-4821CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.emis.de/journals/BAG/vol.46/no.1/b46h1pue.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:02:29Zoai:ri.conicet.gov.ar:11336/240594instacron: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 10:02:29.617CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Conjugacy for closed convex sets
title Conjugacy for closed convex sets
spellingShingle Conjugacy for closed convex sets
Jaume, Daniel Alejandro
CONJUGACY
CLOSED
CONVEX
SETS
title_short Conjugacy for closed convex sets
title_full Conjugacy for closed convex sets
title_fullStr Conjugacy for closed convex sets
title_full_unstemmed Conjugacy for closed convex sets
title_sort Conjugacy for closed convex sets
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 CONJUGACY
CLOSED
CONVEX
SETS
topic CONJUGACY
CLOSED
CONVEX
SETS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Even though the polarity is a well defined operation for arbitrary subsets in the Euclidean n-dimensional space, the related operation of conjugacy of faces appears defined in the literature exclusively for either convex bodies containning the origin as interior point and their polar sets, or for closed convex cones. This paper extends the geometry of closed convex cones and convex bodies to unbounded convex sets (and, in a dual way, to those closed convex sets containing the origin at the boundary), not only for the sake of theoretical completeness, but also for the potential applications of this theory in the fields of Convex Programming and Semi-infinite Programming. Introducing the recession cone into the analysis we develop a general theory of conjugacy which, together with the new concept of curvature index of a convex set on a face, allows us to establish a strong result on complementary dimensions of conjugate faces which extends a well-known result on polytopes.
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 Even though the polarity is a well defined operation for arbitrary subsets in the Euclidean n-dimensional space, the related operation of conjugacy of faces appears defined in the literature exclusively for either convex bodies containning the origin as interior point and their polar sets, or for closed convex cones. This paper extends the geometry of closed convex cones and convex bodies to unbounded convex sets (and, in a dual way, to those closed convex sets containing the origin at the boundary), not only for the sake of theoretical completeness, but also for the potential applications of this theory in the fields of Convex Programming and Semi-infinite Programming. Introducing the recession cone into the analysis we develop a general theory of conjugacy which, together with the new concept of curvature index of a convex set on a face, allows us to establish a strong result on complementary dimensions of conjugate faces which extends a well-known result on polytopes.
publishDate 2005
dc.date.none.fl_str_mv 2005-12
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/11336/240594
Jaume, Daniel Alejandro; Puente, Rubén Oscar; Conjugacy for closed convex sets; Hedelmann Verlag; Beitrage R Algebra Geom; 46; 1; 12-2005; 131-149
0138-4821
CONICET Digital
CONICET
url http://hdl.handle.net/11336/240594
identifier_str_mv Jaume, Daniel Alejandro; Puente, Rubén Oscar; Conjugacy for closed convex sets; Hedelmann Verlag; Beitrage R Algebra Geom; 46; 1; 12-2005; 131-149
0138-4821
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://www.emis.de/journals/BAG/vol.46/no.1/b46h1pue.pdf
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 Hedelmann Verlag
publisher.none.fl_str_mv Hedelmann Verlag
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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