Trends in PDE Constrained Optimization

  • Günter Leugering
  • Peter Benner
  • Sebastian Engell
  • Andreas Griewank
  • Helmut Harbrecht
  • Michael Hinze
  • Rolf Rannacher
  • Stefan Ulbrich

Part of the International Series of Numerical Mathematics book series (ISNM, volume 165)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Günter Leugering, Andreas Griewank, Stefan Ulbrich, Helmut Harbrecht, Peter Benner, Rolf Rannacher et al.
    Pages 1-4
  3. Constrained Optimization, Identification and Control

    1. Front Matter
      Pages 5-5
    2. Luise Blank, M. Hassan Farshbaf-Shaker, Claudia Hecht, Josef Michl, Christoph Rupprecht
      Pages 11-26
    3. Torsten Bosse, Nicolas R. Gauger, Andreas Griewank, Stefanie Günther, Volker Schulz
      Pages 43-66
    4. Torsten Bosse, Nicolas R. Gauger, Andreas Griewank, Stefanie Günther, Lena Kaland, Claudia Kratzenstein et al.
      Pages 67-84
    5. Stefanie Bott, Debora Clever, Jens Lang, Stefan Ulbrich, Jan Carsten Ziems, Dirk Schröder
      Pages 85-108
    6. Sebastian Pfaff, Stefan Ulbrich, Günter Leugering
      Pages 109-131
    7. Michael Hintermüller, Antoine Laurain, Caroline Löbhard, Carlos N. Rautenberg, Thomas M. Surowiec
      Pages 133-153
    8. Karl-Heinz Hoffmann, Nikolai D. Botkin, Varvara L. Turova
      Pages 155-172
    9. Eberhard Bänsch, Peter Benner, Jens Saak, Heiko K. Weichelt
      Pages 173-188
  4. Shape and Topology Optimization

    1. Front Matter
      Pages 189-189
    2. Sergio Conti, Benedict Geihe, Martin Rumpf, Rüdiger Schultz
      Pages 193-211
    3. Helmut Harbrecht, Johannes Tausch
      Pages 213-229
    4. Luise Blank, M. Hassan Farshbaf-Shaker, Harald Garcke, Christoph Rupprecht, Vanessa Styles
      Pages 231-246
  5. Adaptivity and Model Reduction

    1. Front Matter
      Pages 247-247
    2. Peter Benner, Rolf Rannacher
      Pages 249-250
    3. Thomas Apel, Johannes Pfefferer, Arnd Rösch
      Pages 285-302
    4. Peter Benner, Ekkehard Sachs, Stefan Volkwein
      Pages 303-326
    5. Ekkehard W. Sachs, Marina Schneider, Matthias Schu
      Pages 327-342
  6. Discretization: Concepts and Analysis

    1. Front Matter
      Pages 343-343
    2. Malte Braack, Markus Klein, Andreas Prohl, Benjamin Tews
      Pages 347-363
    3. Kristina Kohls, Kunibert G. Siebert, Arnd Rösch
      Pages 403-419
  7. Applications

    1. Front Matter
      Pages 437-437
    2. Günter Leugering, Peter Benner, Sebastian Engell, Andreas Griewank, Helmut Harbrecht, Michael Hinze et al.
      Pages 439-440
    3. Richard C. Barnard, Martin Frank, Michael Herty
      Pages 441-453
    4. Martin Burger, René Pinnau, Marcisse Fouego, Sebastian Rau
      Pages 455-470
    5. Markus Dick, Martin Gugat, Michael Herty, Günter Leugering, Sonja Steffensen, Ke Wang
      Pages 487-504
    6. Thomas Franke, Ronald H. W. Hoppe, Christopher Linsenmann, Lothar Schmid, Achim Wixforth
      Pages 505-519
    7. Malte Behrens, Hans Georg Bock, Sebastian Engell, Phawitphorn Khobkhun, Andreas Potschka
      Pages 521-537
    8. Roland Herzog, Arnd Rösch, Stefan Ulbrich, Winnifried Wollner
      Pages 539-543

About this book


Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored as part of the Deutsche Forschungsgemeinschaft (DFG) priority program 1253 on “Optimization with Partial Differential Equations” from 2006 to 2013. The investigations were motivated by the fascinating potential applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume, contributions from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics.

The book is divided into five sections on “Constrained Optimization, Identification and Control”, “Shape and Topology Optimization”, “Adaptivity and Model Reduction”, “Discretization: Concepts and Analysis” and “Applications”. Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview of topics that set sustainable trends for future research. This makes this special volume interesting not only for mathematicians, but also for engineers and for natural and medical scientists working on processes that can be modeled by PDEs.


adaptivity discretization model reduction optimal control partial differential equations shape and topology optimization

Editors and affiliations

  • Günter Leugering
    • 1
  • Peter Benner
    • 2
  • Sebastian Engell
    • 3
  • Andreas Griewank
    • 4
  • Helmut Harbrecht
    • 5
  • Michael Hinze
    • 6
  • Rolf Rannacher
    • 7
  • Stefan Ulbrich
    • 8
  1. 1.Department MathematikUniversität Erlangen-NürnbergErlangenGermany
  2. 2.Institut für Dynamik komplexer technischMax-Planck-InstitutMagdeburgGermany
  3. 3.Fakultät Bio- und ChemieingenieurwesenTechnische Universität DortmundDortmundGermany
  4. 4.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  5. 5.Mathematisches InstitutUniversität BaselBaselSwitzerland
  6. 6.Fachbereich Mathematik Optimierung und ApproximationUniversität HamburgHamburgGermany
  7. 7.Institut für Angewandte MathematikRuprecht-Karls-Universität HeidelbergHeidelbergGermany
  8. 8.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany

Bibliographic information