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Constrained Optimization and Optimal Control for Partial Differential Equations pp 171–182Cite as

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A Globalized Semi-smooth Newton Method for Variational Discretization of Control Constrained Elliptic Optimal Control Problems

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

Abstract

When combining the numerical concept of variational discretization introduced in [Hin03, Hin05] and semi-smooth Newton methods for the numerical solution of pde constrained optimization with control constraints [HIK03, Ulb03] special emphasis has to be placed on the implementation, convergence and globalization of the numerical algorithm. In the present work we address all these issues following [HV]. In particular we prove fast local convergence of the algorithm and propose a globalization strategy which is applicable in many practically relevant mathematical settings. We illustrate our analytical and algorithmical findings by numerical experiments.

Mathematics Subject Classification (2000). 49J20, 49K20, 49M15.

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References

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Author information

Authors and Affiliations

  1. Schwerpunkt Optimierung und Approximation, Universität Hamburg, Bundesstraße 55, D-20146, Hamburg, Germany

    Michael Hinze & Morten Vierling

Authors
  1. Michael Hinze
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  2. Morten Vierling
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Corresponding author

Correspondence to Michael Hinze .

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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Hinze, M., Vierling, M. (2012). A Globalized Semi-smooth Newton Method for Variational Discretization of Control Constrained Elliptic Optimal Control Problems. 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_9

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