POD-Based Mixed-Integer Optimal Control of the Heat Equation

Lade...
Vorschaubild
Dateien
Zu diesem Dokument gibt es keine Dateien.
Datum
2019
Herausgeber:innen
Kontakt
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
URI (zitierfähiger Link)
ArXiv-ID
Internationale Patentnummer
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Core Facility der Universität Konstanz
Gesperrt bis
Titel in einer weiteren Sprache
Forschungsvorhaben
Organisationseinheiten
Zeitschriftenheft
Publikationstyp
Zeitschriftenartikel
Publikationsstatus
Published
Erschienen in
Zusammenfassung

In the present paper an optimal control problem governed by the heat equation is considered, where continuous as well as discrete controls are involved. To obtain the discrete controls the branch-and-bound method is utilized, where in each node a relaxed control constrained optimal control problem has to be solved involving only continuous controls. However, the solutions to many relaxed optimal control problems have to be computed numerically. For that reason model-order reduction is applied to speed-up the branch-and-bound method. In this work the method of proper orthogonal decomposition (POD) is used. A posteriori error estimation in each node ensures that the calculated solutions are sufficiently accurate. Numerical experiments illustrate the efficiency of the proposed strategy.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
Mixed-integer programming, Optimal control, PDE-constrained optimization, Proper orthogonal decomposition, Error analysis
Konferenz
Rezension
undefined / . - undefined, undefined
Zitieren
ISO 690BACHMANN, Freya, Dennis BEERMANN, Jianjie LU, Stefan VOLKWEIN, 2019. POD-Based Mixed-Integer Optimal Control of the Heat Equation. In: Journal of Scientific Computing. 2019, 81(1), pp. 48-75. ISSN 0885-7474. eISSN 1573-7691. Available under: doi: 10.1007/s10915-019-00924-3
BibTex
@article{Bachmann2019-10PODBa-39073.2,
  year={2019},
  doi={10.1007/s10915-019-00924-3},
  title={POD-Based Mixed-Integer Optimal Control of the Heat Equation},
  number={1},
  volume={81},
  issn={0885-7474},
  journal={Journal of Scientific Computing},
  pages={48--75},
  author={Bachmann, Freya and Beermann, Dennis and Lu, Jianjie and Volkwein, Stefan}
}
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/123456789/39073.2">
    <dc:creator>Bachmann, Freya</dc:creator>
    <dc:contributor>Volkwein, Stefan</dc:contributor>
    <dc:contributor>Beermann, Dennis</dc:contributor>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:creator>Beermann, Dennis</dc:creator>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2019-04-09T15:27:15Z</dc:date>
    <dc:contributor>Bachmann, Freya</dc:contributor>
    <dc:contributor>Lu, Jianjie</dc:contributor>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2019-04-09T15:27:15Z</dcterms:available>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/39073.2"/>
    <dc:language>eng</dc:language>
    <dc:creator>Volkwein, Stefan</dc:creator>
    <dc:creator>Lu, Jianjie</dc:creator>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dcterms:abstract xml:lang="eng">In the present paper an optimal control problem governed by the heat equation is considered, where continuous as well as discrete controls are involved. To obtain the discrete controls the branch-and-bound method is utilized, where in each node a relaxed control constrained optimal control problem has to be solved involving only continuous controls. However, the solutions to many relaxed optimal control problems have to be computed numerically. For that reason model-order reduction is applied to speed-up the branch-and-bound method. In this work the method of proper orthogonal decomposition (POD) is used. A posteriori error estimation in each node ensures that the calculated solutions are sufficiently accurate. Numerical experiments illustrate the efficiency of the proposed strategy.</dcterms:abstract>
    <dcterms:title>POD-Based Mixed-Integer Optimal Control of the Heat Equation</dcterms:title>
    <dcterms:issued>2019-10</dcterms:issued>
    <dc:rights>terms-of-use</dc:rights>
  </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
Ja
Diese Publikation teilen

Versionsgeschichte

Gerade angezeigt 1 - 2 von 2
VersionDatumZusammenfassung
2*
2019-04-09 15:24:54
2017-05-30 14:34:09
* Ausgewählte Version