Optimization of polynomials on compact semialgebraic sets

Kurzanzeige
dc.contributor.authorSchweighofer, Markus
dc.date.accessioned2011-11-09T11:45:01Zdeu
dc.date.available2011-11-09T11:45:01Zdeu
dc.date.issued2005
dc.description.abstractWe give a short introduction to Lasserre's method for minimizing a polynomial on a compact basic closed semialgebraic set. It consists of successively solving tighter and tighter convex relaxations of this problem which can be formulated as semidefinite programs. We give a new short proof for the convergence of the optimal values of these relaxations to the minimum which is constructive and elementary. In the case that there is a unique minimizer, we prove that every sequence of nearly optimal solutions of the successive relaxations gives rise to a sequence of points converging to this minimizer.eng
dc.description.versionpublished
dc.identifier.citationFirst publ. in: SIAM Journal of Optimization 15 (2005), 3. - S. 805-825deu
dc.identifier.doi10.1137/S1052623403431779deu
dc.identifier.ppn352878932deu
dc.identifier.urihttp://kops.uni-konstanz.de/handle/123456789/15647
dc.language.isoengdeu
dc.legacy.dateIssued2011-11-09deu
dc.rightsterms-of-usedeu
dc.rights.urihttps://rightsstatements.org/page/InC/1.0/deu
dc.subjectnonconvex optimizationdeu
dc.subjectpositive polynomialdeu
dc.subjectsum of squaresdeu
dc.subjectmoment problemdeu
dc.subjectPositivstellensatzdeu
dc.subjectsemidefinite programming.deu
dc.subject.ddc510deu
dc.titleOptimization of polynomials on compact semialgebraic setseng
dc.typeJOURNAL_ARTICLEdeu
dspace.entity.typePublication
kops.citation.bibtex
@article{Schweighofer2005Optim-15647,
  year={2005},
  doi={10.1137/S1052623403431779},
  title={Optimization of polynomials on compact semialgebraic sets},
  number={3},
  volume={15},
  issn={1052-6234},
  journal={SIAM Journal on Optimization},
  pages={805--825},
  author={Schweighofer, Markus}
}
kops.citation.iso690SCHWEIGHOFER, Markus, 2005. Optimization of polynomials on compact semialgebraic sets. In: SIAM Journal on Optimization. 2005, 15(3), pp. 805-825. ISSN 1052-6234. Available under: doi: 10.1137/S1052623403431779deu
kops.citation.iso690SCHWEIGHOFER, Markus, 2005. Optimization of polynomials on compact semialgebraic sets. In: SIAM Journal on Optimization. 2005, 15(3), pp. 805-825. ISSN 1052-6234. Available under: doi: 10.1137/S1052623403431779eng
kops.citation.rdf
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/15647">
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:language>eng</dc:language>
    <dc:contributor>Schweighofer, Markus</dc:contributor>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:abstract xml:lang="eng">We give a short introduction to Lasserre's method for minimizing a polynomial on a compact basic closed semialgebraic set. It consists of successively solving tighter and tighter convex relaxations of this problem which can be formulated as semidefinite programs. We give a new short proof for the convergence of the optimal values of these relaxations to the minimum which is constructive and elementary. In the case that there is a unique minimizer, we prove that every sequence of nearly optimal solutions of the successive relaxations gives rise to a sequence of points converging to this minimizer.</dcterms:abstract>
    <dcterms:title>Optimization of polynomials on compact semialgebraic sets</dcterms:title>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-11-09T11:45:01Z</dcterms:available>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:creator>Schweighofer, Markus</dc:creator>
    <dcterms:issued>2005</dcterms:issued>
    <dcterms:bibliographicCitation>First publ. in: SIAM Journal of Optimization 15 (2005), 3. - S. 805-825</dcterms:bibliographicCitation>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/15647/2/convergence.pdf"/>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-11-09T11:45:01Z</dc:date>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/15647/2/convergence.pdf"/>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/15647"/>
    <dc:rights>terms-of-use</dc:rights>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
  </rdf:Description>
</rdf:RDF>
kops.description.openAccessopenaccessgreen
kops.flag.knbibliographytrue
kops.identifier.nbnurn:nbn:de:bsz:352-156477deu
kops.sourcefieldSIAM Journal on Optimization. 2005, <b>15</b>(3), pp. 805-825. ISSN 1052-6234. Available under: doi: 10.1137/S1052623403431779deu
kops.sourcefield.plainSIAM Journal on Optimization. 2005, 15(3), pp. 805-825. ISSN 1052-6234. Available under: doi: 10.1137/S1052623403431779deu
kops.sourcefield.plainSIAM Journal on Optimization. 2005, 15(3), pp. 805-825. ISSN 1052-6234. Available under: doi: 10.1137/S1052623403431779eng
kops.submitter.emailute.otterbeck@uni-konstanz.dedeu
relation.isAuthorOfPublication8b9437c8-6a21-47fb-94b5-170d4d26b628
relation.isAuthorOfPublication.latestForDiscovery8b9437c8-6a21-47fb-94b5-170d4d26b628
source.bibliographicInfo.fromPage805
source.bibliographicInfo.issue3
source.bibliographicInfo.toPage825
source.bibliographicInfo.volume15
source.identifier.issn1052-6234
source.periodicalTitleSIAM Journal on Optimization

Dateien

Originalbündel

Gerade angezeigt 1 - 1 von 1
Vorschaubild nicht verfügbar
Name:
convergence.pdf
Größe:
1.56 MB
Format:
Adobe Portable Document Format
convergence.pdf
convergence.pdfGröße: 1.56 MBDownloads: 787

Lizenzbündel

Gerade angezeigt 1 - 1 von 1
Vorschaubild nicht verfügbar
Name:
license.txt
Größe:
1.92 KB
Format:
Plain Text
Beschreibung:
license.txt
license.txtGröße: 1.92 KBDownloads: 0

Sammlungen

Mathematik und Statistik: Publikationen