First-order augmented Lagrangian methods for state constraint problems

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JEHLE, Jonas Siegfried, 2018. First-order augmented Lagrangian methods for state constraint problems [Master thesis]. Konstanz: Universität Konstanz

@mastersthesis{Jehle2018First-43402, title={First-order augmented Lagrangian methods for state constraint problems}, year={2018}, address={Konstanz}, school={Universität Konstanz}, author={Jehle, Jonas Siegfried} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dcterms:rights rdf:resource=""/> <dcterms:issued>2018</dcterms:issued> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dspace:isPartOfCollection rdf:resource=""/> <dcterms:hasPart rdf:resource=""/> <dcterms:title>First-order augmented Lagrangian methods for state constraint problems</dcterms:title> <dc:date rdf:datatype="">2018-10-01T08:05:00Z</dc:date> <dc:creator>Jehle, Jonas Siegfried</dc:creator> <dc:contributor>Jehle, Jonas Siegfried</dc:contributor> <dc:language>eng</dc:language> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <bibo:uri rdf:resource=""/> <dc:rights>terms-of-use</dc:rights> <dspace:hasBitstream rdf:resource=""/> <dcterms:available rdf:datatype="">2018-10-01T08:05:00Z</dcterms:available> <dcterms:abstract xml:lang="eng">In this thesis, the augmented Lagrangian method is used to solve optimal boundary control problems. The considered optimal control problem appears in energy efficient building operation and consists of a heat equation with convection along with bilateral control and state constraints. The goal is to fit the temperature (state) to a given prescribed temperature profile covering as few heating (controlling) costs as possible. Numerically, a first-order method is applied to solve the minimization problem occurring within the augmented Lagrangian algorithm. Thereto, we set up and solve the adjoint equation. Both partial differential equations, the state and the adjoint equation, are treated with the finite element Galerkin ansatz combined with an implicit Euler scheme in time. At the end, numerical tests of the created first-order augmented Lagrangian method illustrate the efficiency of the proposed strategy.</dcterms:abstract> <dcterms:isPartOf rdf:resource=""/> </rdf:Description> </rdf:RDF>

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