Numerical Analysis of Optimality-System POD for Constrained Optimal Control
| dc.contributor.author | Grimm, Eva | |
| dc.contributor.author | Gubisch, Martin | |
| dc.contributor.author | Volkwein, Stefan | |
| dc.date.accessioned | 2015-12-08T10:01:50Z | |
| dc.date.available | 2015-12-08T10:01:50Z | |
| dc.date.issued | 2015 | eng |
| dc.description.abstract | In this work linear-quadratic optimal control problems for parabolic equations with control and state constraints are considered. Utilizing a Lavrentiev regularization we obtain a linear-quadratic optimal control problem with mixed control-state constraints. For the numerical solution a Galerkin discretization is applied utilizing proper orthogonal decomposition (POD). Based on a perturbation method it is determined by a-posteriori error analysis how far the suboptimal control, computed on the basis of the POD method, is from the (unknown) exact one. POD basis updates are computed by optimality-system POD. Numerical examples illustrate the theoretical results for control and state constrained optimal control problems. | eng |
| dc.description.version | published | eng |
| dc.identifier.doi | 10.1007/978-3-319-22997-3_18 | eng |
| dc.identifier.uri | https://kops.uni-konstanz.de/handle/123456789/32367 | |
| dc.language.iso | eng | eng |
| dc.subject.ddc | 510 | eng |
| dc.title | Numerical Analysis of Optimality-System POD for Constrained Optimal Control | eng |
| dc.type | INPROCEEDINGS | eng |
| dspace.entity.type | Publication | |
| kops.citation.bibtex | @inproceedings{Grimm2015Numer-32367,
year={2015},
doi={10.1007/978-3-319-22997-3_18},
title={Numerical Analysis of Optimality-System POD for Constrained Optimal Control},
number={105},
isbn={978-3-319-22996-6},
issn={1439-7358},
publisher={Springer},
address={Cham [u.a.]},
series={Lecture Notes in Computational Science and Engineering},
booktitle={Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems},
pages={297--317},
editor={Mehl, Miriam},
author={Grimm, Eva and Gubisch, Martin and Volkwein, Stefan}
} | |
| kops.citation.iso690 | GRIMM, Eva, Martin GUBISCH, Stefan VOLKWEIN, 2015. Numerical Analysis of Optimality-System POD for Constrained Optimal Control. 3rd International Workshop on Computational Engineering (CE 2014). Stuttgart, 6. Okt. 2014 - 10. Okt. 2014. In: MEHL, Miriam, ed. and others. Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems. Cham [u.a.]: Springer, 2015, pp. 297-317. Lecture Notes in Computational Science and Engineering. 105. ISSN 1439-7358. eISSN 2197-7100. ISBN 978-3-319-22996-6. Available under: doi: 10.1007/978-3-319-22997-3_18 | deu |
| kops.citation.iso690 | GRIMM, Eva, Martin GUBISCH, Stefan VOLKWEIN, 2015. Numerical Analysis of Optimality-System POD for Constrained Optimal Control. 3rd International Workshop on Computational Engineering (CE 2014). Stuttgart, Oct 6, 2014 - Oct 10, 2014. In: MEHL, Miriam, ed. and others. Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems. Cham [u.a.]: Springer, 2015, pp. 297-317. Lecture Notes in Computational Science and Engineering. 105. ISSN 1439-7358. eISSN 2197-7100. ISBN 978-3-319-22996-6. Available under: doi: 10.1007/978-3-319-22997-3_18 | eng |
| 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/123456789/32367">
<dc:creator>Grimm, Eva</dc:creator>
<dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2015-12-08T10:01:50Z</dc:date>
<dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2015-12-08T10:01:50Z</dcterms:available>
<dc:creator>Gubisch, Martin</dc:creator>
<bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/32367"/>
<dcterms:abstract xml:lang="eng">In this work linear-quadratic optimal control problems for parabolic equations with control and state constraints are considered. Utilizing a Lavrentiev regularization we obtain a linear-quadratic optimal control problem with mixed control-state constraints. For the numerical solution a Galerkin discretization is applied utilizing proper orthogonal decomposition (POD). Based on a perturbation method it is determined by a-posteriori error analysis how far the suboptimal control, computed on the basis of the POD method, is from the (unknown) exact one. POD basis updates are computed by optimality-system POD. Numerical examples illustrate the theoretical results for control and state constrained optimal control problems.</dcterms:abstract>
<dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
<void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
<foaf:homepage rdf:resource="http://localhost:8080/"/>
<dc:creator>Volkwein, Stefan</dc:creator>
<dc:contributor>Grimm, Eva</dc:contributor>
<dc:contributor>Gubisch, Martin</dc:contributor>
<dcterms:title>Numerical Analysis of Optimality-System POD for Constrained Optimal Control</dcterms:title>
<dc:contributor>Volkwein, Stefan</dc:contributor>
<dcterms:issued>2015</dcterms:issued>
<dc:language>eng</dc:language>
<dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
</rdf:Description>
</rdf:RDF> | |
| kops.conferencefield | 3rd International Workshop on Computational Engineering (CE 2014), 6. Okt. 2014 - 10. Okt. 2014, Stuttgart | deu |
| kops.date.conferenceEnd | 2014-10-10 | eng |
| kops.date.conferenceStart | 2014-10-06 | eng |
| kops.flag.knbibliography | true | |
| kops.location.conference | Stuttgart | eng |
| kops.sourcefield | MEHL, Miriam, ed. and others. <i>Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems</i>. Cham [u.a.]: Springer, 2015, pp. 297-317. Lecture Notes in Computational Science and Engineering. 105. ISSN 1439-7358. eISSN 2197-7100. ISBN 978-3-319-22996-6. Available under: doi: 10.1007/978-3-319-22997-3_18 | deu |
| kops.sourcefield.plain | MEHL, Miriam, ed. and others. Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems. Cham [u.a.]: Springer, 2015, pp. 297-317. Lecture Notes in Computational Science and Engineering. 105. ISSN 1439-7358. eISSN 2197-7100. ISBN 978-3-319-22996-6. Available under: doi: 10.1007/978-3-319-22997-3_18 | deu |
| kops.sourcefield.plain | MEHL, Miriam, ed. and others. Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems. Cham [u.a.]: Springer, 2015, pp. 297-317. Lecture Notes in Computational Science and Engineering. 105. ISSN 1439-7358. eISSN 2197-7100. ISBN 978-3-319-22996-6. Available under: doi: 10.1007/978-3-319-22997-3_18 | eng |
| kops.title.conference | 3rd International Workshop on Computational Engineering (CE 2014) | eng |
| relation.isAuthorOfPublication | 86bea439-a257-4a07-82a8-bf53b4651c92 | |
| relation.isAuthorOfPublication | e9bc68c9-e2ac-40a9-b319-9d8deb7f8ca5 | |
| relation.isAuthorOfPublication | 1331ea51-1e11-44de-851e-280a04907915 | |
| relation.isAuthorOfPublication.latestForDiscovery | 86bea439-a257-4a07-82a8-bf53b4651c92 | |
| source.bibliographicInfo.fromPage | 297 | eng |
| source.bibliographicInfo.seriesNumber | 105 | eng |
| source.bibliographicInfo.toPage | 317 | eng |
| source.contributor.editor | Mehl, Miriam | |
| source.flag.etalEditor | true | eng |
| source.identifier.eissn | 2197-7100 | eng |
| source.identifier.isbn | 978-3-319-22996-6 | eng |
| source.identifier.issn | 1439-7358 | eng |
| source.publisher | Springer | eng |
| source.publisher.location | Cham [u.a.] | eng |
| source.relation.ispartofseries | Lecture Notes in Computational Science and Engineering | eng |
| source.title | Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems | eng |