Fast Solution Techniques in Constrained Optimal Boundary Control of the Semilinear Heat Equation

Hintermüller, Michael; Volkwein, Stefan; Diwoky, Franz

Fast Solution Techniques in Constrained Optimal Boundary Control of the Semilinear Heat Equation

Files

There are no files associated with this item.

Date

2007

Authors

Hintermüller, Michael

Volkwein, Stefan

Diwoky, Franz

DOI (citable link)

10.1007/978-3-7643-7721-2_6

Collections

Mathematik und Statistik

Publication type

Contribution to a collection

Publication status

Published

Published in

Control of Coupled Partial Differential Equations / Kunisch, Karl et al. (ed.). - Basel : Birkhäuser, 2007. - (International Series of Numerical Mathematics ; 155). - pp. 119-147. - ISBN 978-3-7643-7720-5

Abstract

Efficient numerical techniques for the solution of constrained optimal control problems for the nonlinear heat equation are considered. The nonlinearity in the governing equation is due to the boundary conditions which cover the Boltzmann radiation boundary condition. With respect to numerical algorithms, variants of semismooth Newton methods are proposed which allow a convergence analysis in function space. For the latter aspect the concept of generalized (Newton, or slant) differentiability is invoked. The paper ends with a comparison of the proposed algorithms among each other and with a sequential quadratic programming method.

Subject (DDC)

510 Mathematics

Keywords

Constrained optimal control, integral constraints, nonlinear heat equation, pointwise constraints, semismooth Newton

Cite This

ISO 690

HINTERMÜLLER, Michael, Stefan VOLKWEIN, Franz DIWOKY, 2007. Fast Solution Techniques in Constrained Optimal Boundary Control of the Semilinear Heat Equation. In: KUNISCH, Karl, ed. and others. Control of Coupled Partial Differential Equations. Basel:Birkhäuser, pp. 119-147. ISBN 978-3-7643-7720-5. Available under: doi: 10.1007/978-3-7643-7721-2_6

BibTex

@incollection{Hintermuller2007Solut-41215,
  year={2007},
  doi={10.1007/978-3-7643-7721-2_6},
  title={Fast Solution Techniques in Constrained Optimal Boundary Control of the Semilinear Heat Equation},
  number={155},
  isbn={978-3-7643-7720-5},
  publisher={Birkhäuser},
  address={Basel},
  series={International Series of Numerical Mathematics},
  booktitle={Control of Coupled Partial Differential Equations},
  pages={119--147},
  editor={Kunisch, Karl},
  author={Hintermüller, Michael and Volkwein, Stefan and Diwoky, Franz}
}

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/123456789/41215">
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2018-02-02T12:58:26Z</dc:date>
    <dc:language>eng</dc:language>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/41215"/>
    <dcterms:abstract xml:lang="eng">Efficient numerical techniques for the solution of constrained optimal control problems for the nonlinear heat equation are considered. The nonlinearity in the governing equation is due to the boundary conditions which cover the Boltzmann radiation boundary condition. With respect to numerical algorithms, variants of semismooth Newton methods are proposed which allow a convergence analysis in function space. For the latter aspect the concept of generalized (Newton, or slant) differentiability is invoked. The paper ends with a comparison of the proposed algorithms among each other and with a sequential quadratic programming method.</dcterms:abstract>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:creator>Volkwein, Stefan</dc:creator>
    <dc:contributor>Hintermüller, Michael</dc:contributor>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:issued>2007</dcterms:issued>
    <dc:creator>Diwoky, Franz</dc:creator>
    <dc:contributor>Diwoky, Franz</dc:contributor>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:contributor>Volkwein, Stefan</dc:contributor>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2018-02-02T12:58:26Z</dcterms:available>
    <dcterms:title>Fast Solution Techniques in Constrained Optimal Boundary Control of the Semilinear Heat Equation</dcterms:title>
    <dc:creator>Hintermüller, Michael</dc:creator>
  </rdf:Description>
</rdf:RDF>

Bibliography of Konstanz

No