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POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems

POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems

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KAHLBACHER, Martin, Stefan VOLKWEIN, 2011. POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems. In: ESAIM: Mathematical Modelling and Numerical Analysis. 46(2), pp. 491-511. ISSN 0764-583X

@article{Kahlbacher2011a-pos-18558, title={POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems}, year={2011}, doi={10.1051/m2an/2011061}, number={2}, volume={46}, issn={0764-583X}, journal={ESAIM: Mathematical Modelling and Numerical Analysis}, pages={491--511}, author={Kahlbacher, Martin and Volkwein, Stefan} }

<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/18558"> <dcterms:bibliographicCitation>First publ. in: ESAIM : Mathematical Modelling and Numerical Analysis ; 46 (2012), 2. - pp. 491-511</dcterms:bibliographicCitation> <dc:rights>deposit-license</dc:rights> <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/18558"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2012-02-20T12:09:03Z</dc:date> <dcterms:rights rdf:resource="http://nbn-resolving.org/urn:nbn:de:bsz:352-20140905103605204-4002607-1"/> <dcterms:title>POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems</dcterms:title> <dc:creator>Volkwein, Stefan</dc:creator> <dcterms:issued>2011</dcterms:issued> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2012-02-20T12:09:03Z</dcterms:available> <dc:language>eng</dc:language> <dc:creator>Kahlbacher, Martin</dc:creator> <dc:contributor>Kahlbacher, Martin</dc:contributor> <dc:contributor>Volkwein, Stefan</dc:contributor> <dcterms:abstract xml:lang="eng">An optimal control problem governed by a bilinear elliptic equation is considered. This problem is solved by the sequential quadratic programming (SQP) method in an infinite-dimensional framework. In each level of this iterative method the solution of linear-quadratic subproblem is computed by a Galerkin projection using proper orthogonal decomposition (POD). Thus, an approximate (inexact) solution of the subproblem is determined. Based on a POD a-posteriori error estimator developed by Tröltzsch and Volkwein [Comput. Opt. Appl. 44 (2009) 83–115] the difference of the suboptimal to the (unknown) optimal solution of the linear-quadratic subproblem is estimated. Hence, the inexactness of the discrete solution is controlled in such a way that locally superlinear or even quadratic rate of convergence of the SQP is ensured. Numerical examples illustrate the efficiency for the proposed approach.</dcterms:abstract> </rdf:Description> </rdf:RDF>

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