An exact duality theory for semidefinite programming based on sums of squares

Lade...
Vorschaubild
Dateien
Zu diesem Dokument gibt es keine Dateien.
Datum
2013
Herausgeber:innen
Kontakt
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
ArXiv-ID
Internationale Patentnummer
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Core Facility der Universität Konstanz
Gesperrt bis
Titel in einer weiteren Sprache
Publikationstyp
Zeitschriftenartikel
Publikationsstatus
Published
Erschienen in
Mathematics of Operations Research. 2013, 38(3), pp. 569-590. ISSN 0364-765X. eISSN 1526-5471. Available under: doi: 10.1287/moor.1120.0584
Zusammenfassung

Farkas' lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear matrix inequalities. We provide nonlinear algebraic certificates for all infeasible linear matrix inequalities in the spirit of real algebraic geometry: A linear matrix inequality A(x) >_ 0 is infeasible if and only if −1 lies in the quadratic module associated to A. We also present a new exact duality theory for semidefinite programming, motivated by the real radical and sums of squares certificates from real algebraic geometry.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
linear matrix inequality, LMI, spectrahedron, semidefinite programming, SDP, quadratic module, infeasibility, duality theory, real radical, Farkas' lemma
Konferenz
Rezension
undefined / . - undefined, undefined
Forschungsvorhaben
Organisationseinheiten
Zeitschriftenheft
Datensätze
Zitieren
ISO 690SCHWEIGHOFER, Markus, Igor KLEP, 2013. An exact duality theory for semidefinite programming based on sums of squares. In: Mathematics of Operations Research. 2013, 38(3), pp. 569-590. ISSN 0364-765X. eISSN 1526-5471. Available under: doi: 10.1287/moor.1120.0584
BibTex
@article{Schweighofer2013exact-24805,
  year={2013},
  doi={10.1287/moor.1120.0584},
  title={An exact duality theory for semidefinite programming based on sums of squares},
  number={3},
  volume={38},
  issn={0364-765X},
  journal={Mathematics of Operations Research},
  pages={569--590},
  author={Schweighofer, Markus and Klep, Igor}
}
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/123456789/24805">
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/24805"/>
    <dcterms:abstract xml:lang="eng">Farkas' lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear matrix inequalities. We provide nonlinear algebraic certificates for all infeasible linear matrix inequalities in the spirit of real algebraic geometry: A linear matrix inequality A(x) &gt;_ 0 is infeasible if and only if −1 lies in the quadratic module associated to A. We also present a new exact duality theory for semidefinite programming, motivated by the real radical and sums of squares certificates from real algebraic geometry.</dcterms:abstract>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dcterms:issued>2013</dcterms:issued>
    <dcterms:title>An exact duality theory for semidefinite programming based on sums of squares</dcterms:title>
    <dc:contributor>Schweighofer, Markus</dc:contributor>
    <dcterms:bibliographicCitation>Mathematics of Operations Research ;  38 (2013), 3. - S. 569-590</dcterms:bibliographicCitation>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-10-11T14:29:51Z</dc:date>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-10-11T14:29:51Z</dcterms:available>
    <dc:creator>Klep, Igor</dc:creator>
    <dc:rights>terms-of-use</dc:rights>
    <dc:language>eng</dc:language>
    <dc:creator>Schweighofer, Markus</dc:creator>
    <dc:contributor>Klep, Igor</dc:contributor>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
  </rdf:Description>
</rdf:RDF>
Interner Vermerk
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Kontakt
URL der Originalveröffentl.
Prüfdatum der URL
Prüfungsdatum der Dissertation
Finanzierungsart
Kommentar zur Publikation
Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Ja
Begutachtet
Diese Publikation teilen