Utilize este identificador para referenciar este registo:
https://hdl.handle.net/10316/44180
Campo DC | Valor | Idioma |
---|---|---|
dc.contributor.author | Blekherman, Grigoriy | - |
dc.contributor.author | Gouveia, João | - |
dc.contributor.author | Pfeiffer, James | - |
dc.date.accessioned | 2017-10-26T10:58:25Z | - |
dc.date.issued | 2016 | - |
dc.identifier.uri | https://hdl.handle.net/10316/44180 | - |
dc.description.abstract | Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of squares of rational functions modulo the vanishing ideal I(X). From the point of view of applications, such as polynomial optimization, we are interested in rational function representations of small degree. We derive a general upper bound in terms of the Hilbert function of X, and we show that this upper bound is tight for the case of quadratic functions on the hypercube C={0,1}^n, a very well studied case in combinatorial optimization. Using the lower bounds for C we construct a family of globally nonnegative quartic polynomials, which are not sums of squares of rational functions of small degree. To our knowledge this is the first construction for Hilbert’s 17th problem of a family of polynomials of bounded degree which need increasing degrees in rational function representations as the number of variables n goes to infinity. We note that representation theory of the symmetric group S_n plays a crucial role in our proofs of the lower bounds. | por |
dc.language.iso | eng | por |
dc.publisher | Springer | por |
dc.relation | info:eu-repo/grantAgreement/FCT/5876/147205/PT | por |
dc.rights | embargoedAccess | - |
dc.title | Sums of squares on the hypercube | por |
dc.type | article | - |
degois.publication.firstPage | 41 | por |
degois.publication.lastPage | 54 | por |
degois.publication.issue | 1-2 | por |
degois.publication.title | Mathematische Zeitschrift | por |
dc.relation.publisherversion | https://doi.org/10.1007/s00209-016-1644-7 | por |
dc.peerreviewed | yes | por |
dc.identifier.doi | 10.1007/s00209-016-1644-7 | por |
dc.identifier.doi | 10.1007/s00209-016-1644-7 | - |
degois.publication.volume | 284 | por |
dc.date.embargo | 2018-10-26T10:58:25Z | - |
uc.controloAutoridade | Sim | - |
item.openairetype | article | - |
item.fulltext | Com Texto completo | - |
item.languageiso639-1 | en | - |
item.grantfulltext | open | - |
item.cerifentitytype | Publications | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
crisitem.author.researchunit | CMUC - Centre for Mathematics of the University of Coimbra | - |
crisitem.author.orcid | 0000-0001-8345-9754 | - |
Aparece nas coleções: | I&D CMUC - Artigos em Revistas Internacionais |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
---|---|---|---|---|
SquaresHypercubeRevised.pdf | 308.25 kB | Adobe PDF | Ver/Abrir |
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