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Numerical Analysis of State-constrained Optimal Control Problems for PDEs

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Constrained Optimization and Optimal Control for Partial Differential Equations

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 160))

Abstract

We survey the results of SPP 1253 project “Numerical Analysis of State-constrained Optimal Control Problems for PDEs”. In the first part, we consider Lavrentiev-type regularization of both distributed and boundary control. In the second part, we present a priori error estimates for elliptic control problems with finite-dimensional control space and state-constraints both in finitely many points and in all points of a subdomain with nonempty interior.

Mathematics Subject Classification (2000). 49K20, 49M05, 90C06, 90C34, 90C30.

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, D-10623, Berlin, Germany

    Ira Neitzel & Fredi Tröltzsch

Authors
  1. Ira Neitzel
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  2. Fredi Tröltzsch
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Corresponding author

Correspondence to Ira Neitzel .

Editor information

Editors and Affiliations

  1. , Department Mathematik, Universität Erlangen-Nürnberg, Martensstr. 3, Erlangen, 91058, Germany

    Günter Leugering

  2. , Fakultät Bio- und Chemieingenieurwesen, Technische Universität Dortmund, Geschossbau 2, Dortmund, 44221, Germany

    Sebastian Engell

  3. , Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, Berlin, 12489, Germany

    Andreas Griewank

  4. , Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, Hamburg, 20146, Germany

    Michael Hinze

  5. , Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 293, Heidelberg, 69120, Germany

    Rolf Rannacher

  6. , FB 4 - Department Mathematik, Universität Trier, Trier, 54286, Germany

    Volker Schulz

  7. Fakultät für Mathematik, M1, Lehrstuhl für Mathematische Optimierung, Technische Universität München, Boltzmannstr. 3, Garching bei München, 85748, Germany

    Michael Ulbrich

  8. , Fachbereich Mathematik, Technische Universität Darmstadt, Dolivostrasse 15, Darmstadt, 64293, Germany

    Stefan Ulbrich

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Neitzel, I., Tröltzsch, F. (2012). Numerical Analysis of State-constrained Optimal Control Problems for PDEs. In: Leugering, G., et al. Constrained Optimization and Optimal Control for Partial Differential Equations. International Series of Numerical Mathematics, vol 160. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0133-1_24

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