Publikation: Efficient Stochastic Descent Methods for PDE-Constrained Optimization with Uncertain Coefficients
Dateien
Datum
Autor:innen
Herausgeber:innen
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
URI (zitierfähiger Link)
Internationale Patentnummer
Link zur Lizenz
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Sammlungen
Core Facility der Universität Konstanz
Titel in einer weiteren Sprache
Publikationstyp
Publikationsstatus
Erschienen in
Zusammenfassung
In this thesis, we consider a convex, elliptic PDE-constrained optimal control problem that is subject to uncertainty. To solve this problem numerically we use three stochastic descent methods, namely the Stochastic Gradient method, the Stochastic Variance Reduced Gradient method and the Stochastic Adaptive Sampling method. We state theoretical convergence results for the three stochastic descent methods and present a setting in which we conduct numerical tests to compare the convergence behaviour and the CPU time. The numerical experiments show that a modification of the Stochastic Adaptive Sampling method in combination with the Barzilai-Borwein step size rule is the superior choice for the specific problem.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
Schlagwörter
Konferenz
Rezension
Zitieren
ISO 690
FEINEIS, Calvin, 2021. Efficient Stochastic Descent Methods for PDE-Constrained Optimization with Uncertain Coefficients [Master thesis]. Konstanz: Universität KonstanzBibTex
@mastersthesis{Feineis2021Effic-53934, year={2021}, title={Efficient Stochastic Descent Methods for PDE-Constrained Optimization with Uncertain Coefficients}, address={Konstanz}, school={Universität Konstanz}, author={Feineis, Calvin} }
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/123456789/53934"> <dc:language>eng</dc:language> <dc:creator>Feineis, Calvin</dc:creator> <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/53934/3/Feineis_2-171a3bcqba3tk2.pdf"/> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-06-10T05:38:45Z</dcterms:available> <dcterms:title>Efficient Stochastic Descent Methods for PDE-Constrained Optimization with Uncertain Coefficients</dcterms:title> <dc:rights>terms-of-use</dc:rights> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-06-10T05:38:45Z</dc:date> <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:abstract xml:lang="eng">In this thesis, we consider a convex, elliptic PDE-constrained optimal control problem that is subject to uncertainty. To solve this problem numerically we use three stochastic descent methods, namely the Stochastic Gradient method, the Stochastic Variance Reduced Gradient method and the Stochastic Adaptive Sampling method. We state theoretical convergence results for the three stochastic descent methods and present a setting in which we conduct numerical tests to compare the convergence behaviour and the CPU time. The numerical experiments show that a modification of the Stochastic Adaptive Sampling method in combination with the Barzilai-Borwein step size rule is the superior choice for the specific problem.</dcterms:abstract> <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/53934/3/Feineis_2-171a3bcqba3tk2.pdf"/> <foaf:homepage rdf:resource="http://localhost:8080/"/> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/53934"/> <dc:contributor>Feineis, Calvin</dc:contributor> <dcterms:issued>2021</dcterms:issued> </rdf:Description> </rdf:RDF>