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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/14866
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T10:23:35Zoai: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:34982025-09-29 10:23:35.948CONICET 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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1844614231167598592 |
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13.070432 |