Intrinsic complexity estimates in polynomial optimization

Autores
Bank, Bernd; Giusti, Marc; Heintz, Joos Ulrich; Safey El Din, Mohab
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using (sd) O(n) arithmetic operations, where n and s are the numbers of variables and constraints and d is the maximal degree of the polynomials involved. Subject to certain conditions, we associate to each of these problems an intrinsic system degree which becomes in worst case of order (nd) O(n) and which measures the intrinsic complexity of the task under consideration. We design non-uniform deterministic or uniform probabilistic algorithms of intrinsic, quasi-polynomial complexity which solve these problems.
Fil: Bank, Bernd. Universität zu Berlin; Alemania
Fil: Giusti, Marc. Ecole Polytechnique; Francia
Fil: Heintz, Joos Ulrich. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad de Cantabria; España. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Safey El Din, Mohab. Universite Pierre et Marie Curie; Francia
Materia
DEGREE OF VARIETIES
INTRINSIC COMPLEXITY
POLYNOMIAL OPTIMIZATION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/84333
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/84333
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Intrinsic complexity estimates in polynomial optimizationBank, BerndGiusti, MarcHeintz, Joos UlrichSafey El Din, MohabDEGREE OF VARIETIESINTRINSIC COMPLEXITYPOLYNOMIAL OPTIMIZATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using (sd) O(n) arithmetic operations, where n and s are the numbers of variables and constraints and d is the maximal degree of the polynomials involved. Subject to certain conditions, we associate to each of these problems an intrinsic system degree which becomes in worst case of order (nd) O(n) and which measures the intrinsic complexity of the task under consideration. We design non-uniform deterministic or uniform probabilistic algorithms of intrinsic, quasi-polynomial complexity which solve these problems.Fil: Bank, Bernd. Universität zu Berlin; AlemaniaFil: Giusti, Marc. Ecole Polytechnique; FranciaFil: Heintz, Joos Ulrich. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad de Cantabria; España. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Safey El Din, Mohab. Universite Pierre et Marie Curie; FranciaAcademic Press Inc Elsevier Science2014-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84333Bank, Bernd; Giusti, Marc; Heintz, Joos Ulrich; Safey El Din, Mohab; Intrinsic complexity estimates in polynomial optimization; Academic Press Inc Elsevier Science; Journal Of Complexity; 30; 4; 2-2014; 430-4430885-064XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jco.2014.02.005info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0885064X1400020Xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:08:33Zoai:ri.conicet.gov.ar:11336/84333instacron: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 10:08:34.238CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Intrinsic complexity estimates in polynomial optimization
title Intrinsic complexity estimates in polynomial optimization
spellingShingle Intrinsic complexity estimates in polynomial optimization
Bank, Bernd
DEGREE OF VARIETIES
INTRINSIC COMPLEXITY
POLYNOMIAL OPTIMIZATION
title_short Intrinsic complexity estimates in polynomial optimization
title_full Intrinsic complexity estimates in polynomial optimization
title_fullStr Intrinsic complexity estimates in polynomial optimization
title_full_unstemmed Intrinsic complexity estimates in polynomial optimization
title_sort Intrinsic complexity estimates in polynomial optimization
dc.creator.none.fl_str_mv Bank, Bernd
Giusti, Marc
Heintz, Joos Ulrich
Safey El Din, Mohab
author Bank, Bernd
author_facet Bank, Bernd
Giusti, Marc
Heintz, Joos Ulrich
Safey El Din, Mohab
author_role author
author2 Giusti, Marc
Heintz, Joos Ulrich
Safey El Din, Mohab
author2_role author
author
author
dc.subject.none.fl_str_mv DEGREE OF VARIETIES
INTRINSIC COMPLEXITY
POLYNOMIAL OPTIMIZATION
topic DEGREE OF VARIETIES
INTRINSIC COMPLEXITY
POLYNOMIAL OPTIMIZATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using (sd) O(n) arithmetic operations, where n and s are the numbers of variables and constraints and d is the maximal degree of the polynomials involved. Subject to certain conditions, we associate to each of these problems an intrinsic system degree which becomes in worst case of order (nd) O(n) and which measures the intrinsic complexity of the task under consideration. We design non-uniform deterministic or uniform probabilistic algorithms of intrinsic, quasi-polynomial complexity which solve these problems.
Fil: Bank, Bernd. Universität zu Berlin; Alemania
Fil: Giusti, Marc. Ecole Polytechnique; Francia
Fil: Heintz, Joos Ulrich. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad de Cantabria; España. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Safey El Din, Mohab. Universite Pierre et Marie Curie; Francia
description It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using (sd) O(n) arithmetic operations, where n and s are the numbers of variables and constraints and d is the maximal degree of the polynomials involved. Subject to certain conditions, we associate to each of these problems an intrinsic system degree which becomes in worst case of order (nd) O(n) and which measures the intrinsic complexity of the task under consideration. We design non-uniform deterministic or uniform probabilistic algorithms of intrinsic, quasi-polynomial complexity which solve these problems.
publishDate 2014
dc.date.none.fl_str_mv 2014-02
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/11336/84333
Bank, Bernd; Giusti, Marc; Heintz, Joos Ulrich; Safey El Din, Mohab; Intrinsic complexity estimates in polynomial optimization; Academic Press Inc Elsevier Science; Journal Of Complexity; 30; 4; 2-2014; 430-443
0885-064X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84333
identifier_str_mv Bank, Bernd; Giusti, Marc; Heintz, Joos Ulrich; Safey El Din, Mohab; Intrinsic complexity estimates in polynomial optimization; Academic Press Inc Elsevier Science; Journal Of Complexity; 30; 4; 2-2014; 430-443
0885-064X
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.jco.2014.02.005
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0885064X1400020X
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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_ 1842270049737375744
score 13.13397

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