On the minimum of a polynomial function on a basic closed semialgebraic set and applications

Autores
Jeronimo, Gabriela Tali; Perrucci, Daniel Roberto; Tsigaridas, Elias
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is not zero. We also present extensions of these results to noncompact situations. As an application, we obtain a lower bound for the separation of two disjoint connected components of basic closed semialgebraic sets, when at least one of them is compact.
Fil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Perrucci, Daniel Roberto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Tsigaridas, Elias. Universite Pierre et Marie Curie; Francia
Materia
Polynomial Optimization
Effectivity
Semi-Algebraic 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:11336/14866
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/14866
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network_name_str CONICET Digital (CONICET)
spelling On the minimum of a polynomial function on a basic closed semialgebraic set and applicationsJeronimo, Gabriela TaliPerrucci, Daniel RobertoTsigaridas, EliasPolynomial OptimizationEffectivitySemi-Algebraic Setshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is not zero. We also present extensions of these results to noncompact situations. As an application, we obtain a lower bound for the separation of two disjoint connected components of basic closed semialgebraic sets, when at least one of them is compact.Fil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Perrucci, Daniel Roberto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Tsigaridas, Elias. Universite Pierre et Marie Curie; FranciaSiam Publications2013-04info: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/11336/14866Jeronimo, Gabriela Tali; Perrucci, Daniel Roberto; Tsigaridas, Elias; On the minimum of a polynomial function on a basic closed semialgebraic set and applications; Siam Publications; Siam Journal On Optimization; 23; 1; 4-2013; 241-2551052-6234enginfo:eu-repo/semantics/altIdentifier/url/http://epubs.siam.org/doi/abs/10.1137/110857751info:eu-repo/semantics/altIdentifier/doi/10.1137/110857751info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:56:21Zoai:ri.conicet.gov.ar:11336/14866instacron: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:34982025-10-22 11:56:22.184CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the minimum of a polynomial function on a basic closed semialgebraic set and applications
title On the minimum of a polynomial function on a basic closed semialgebraic set and applications
spellingShingle On the minimum of a polynomial function on a basic closed semialgebraic set and applications
Jeronimo, Gabriela Tali
Polynomial Optimization
Effectivity
Semi-Algebraic Sets
title_short On the minimum of a polynomial function on a basic closed semialgebraic set and applications
title_full On the minimum of a polynomial function on a basic closed semialgebraic set and applications
title_fullStr On the minimum of a polynomial function on a basic closed semialgebraic set and applications
title_full_unstemmed On the minimum of a polynomial function on a basic closed semialgebraic set and applications
title_sort On the minimum of a polynomial function on a basic closed semialgebraic set and applications
dc.creator.none.fl_str_mv Jeronimo, Gabriela Tali
Perrucci, Daniel Roberto
Tsigaridas, Elias
author Jeronimo, Gabriela Tali
author_facet Jeronimo, Gabriela Tali
Perrucci, Daniel Roberto
Tsigaridas, Elias
author_role author
author2 Perrucci, Daniel Roberto
Tsigaridas, Elias
author2_role author
author
dc.subject.none.fl_str_mv Polynomial Optimization
Effectivity
Semi-Algebraic Sets
topic Polynomial Optimization
Effectivity
Semi-Algebraic 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 We give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is not zero. We also present extensions of these results to noncompact situations. As an application, we obtain a lower bound for the separation of two disjoint connected components of basic closed semialgebraic sets, when at least one of them is compact.
Fil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Perrucci, Daniel Roberto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Tsigaridas, Elias. Universite Pierre et Marie Curie; Francia
description We give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is not zero. We also present extensions of these results to noncompact situations. As an application, we obtain a lower bound for the separation of two disjoint connected components of basic closed semialgebraic sets, when at least one of them is compact.
publishDate 2013
dc.date.none.fl_str_mv 2013-04
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/11336/14866
Jeronimo, Gabriela Tali; Perrucci, Daniel Roberto; Tsigaridas, Elias; On the minimum of a polynomial function on a basic closed semialgebraic set and applications; Siam Publications; Siam Journal On Optimization; 23; 1; 4-2013; 241-255
1052-6234
url http://hdl.handle.net/11336/14866
identifier_str_mv Jeronimo, Gabriela Tali; Perrucci, Daniel Roberto; Tsigaridas, Elias; On the minimum of a polynomial function on a basic closed semialgebraic set and applications; Siam Publications; Siam Journal On Optimization; 23; 1; 4-2013; 241-255
1052-6234
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://epubs.siam.org/doi/abs/10.1137/110857751
info:eu-repo/semantics/altIdentifier/doi/10.1137/110857751
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 Siam Publications
publisher.none.fl_str_mv Siam Publications
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 12.982451

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