Constrained Optimization and Optimal Control for Partial Differential Equations

  • Günter Leugering
  • Sebastian Engell
  • Andreas Griewank
  • Michael Hinze
  • Rolf Rannacher
  • Volker Schulz
  • Michael Ulbrich
  • Stefan Ulbrich

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Constrained Optimization, Identification and Control

    1. Front Matter
      Pages 1-3
    2. Luise Blank, Martin Butz, Harald Garcke, Lavinia Sarbu, Vanessa Styles
      Pages 21-35
    3. Hans Georg Bock, Andreas Potschka, Sebastian Sager, Johannes P. Schlöder
      Pages 37-49
    4. Thomas Franke, Ronald H. W. Hoppe, Christopher Linsenmann, Achim Wixforth
      Pages 75-98
    5. Nicolas Gauger, Andreas Griewank, Adel Hamdi, Claudia Kratzenstein, Emre Özkaya, Thomas Slawig
      Pages 99-122
    6. Martin Gugat, Michael Herty, Axel Klar, Günther Leugering, Veronika Schleper
      Pages 123-146
    7. Michael Hinze, Michael Köster, Stefan Turek
      Pages 147-170
    8. Denise Holfeld, Philipp Stumm, Andrea Walther
      Pages 183-196
  3. Shape and Topology Optimization

    1. Front Matter
      Pages 213-214
    2. Pradeep Atwal, Sergio Conti, Benedict Geihe, Martin Pach, Martin Rumpf, Rüdiger Schultz
      Pages 215-243
    3. Luise Blank, Harald Garcke, Lavinia Sarbu, Tarin Srisupattarawanit, Vanessa Styles, Axel Voigt
      Pages 245-256
    4. Christian Brandenburg, Florian Lindemann, Michael Ulbrich, Stefan Ulbrich
      Pages 257-275
    5. Karsten Eppler, Helmut Harbrecht
      Pages 277-288
    6. Nicolas Gauger, Caslav Ilic, Stephan Schmidt, Volker Schulz
      Pages 289-300
  4. Model Reduction

    1. Front Matter
      Pages 301-302
  5. Discretization: Concepts and Analysis

  6. Applications

    1. Front Matter
      Pages 483-485
    2. Inga Altrogge, Christof Büskens, Tim Kröger, Heinz-Otto Peitgen, Tobias Preusser, Hanne Tiesler
      Pages 487-499
    3. Eberhard Bänsch, Manfred Kaltenbacher, Günter Leugering, Fabian Schury, Fabian Wein
      Pages 501-519
    4. Nikolai D. Botkin, Karl-Heinz Hoffmann, Varvara L. Turova
      Pages 521-540
    5. Frank Haußer, Sandra Janssen, Axel Voigt
      Pages 561-572
    6. Achim Küpper, Sebastian Engell
      Pages 573-596
    7. René Pinnau, Norbert Siedow
      Pages 597-609
    8. Markus Probst, Michael Lülfesmann, Mike Nicolai, H. Martin Bücker, Marek Behr, Christian H. Bischof
      Pages 611-622

About this book


This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.

Editors and affiliations

  • Günter Leugering
    • 1
  • Sebastian Engell
    • 2
  • Andreas Griewank
    • 3
  • Michael Hinze
    • 4
  • Rolf Rannacher
    • 5
  • Volker Schulz
    • 6
  • Michael Ulbrich
    • 7
  • Stefan Ulbrich
    • 8
  1. 1., Department MathematikUniversität Erlangen-NürnbergErlangenGermany
  2. 2., Fakultät Bio- und ChemieingenieurwesenTechnische Universität DortmundDortmundGermany
  3. 3., Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  4. 4., Fachbereich MathematikUniversität HamburgHamburgGermany
  5. 5., Institut für Angewandte MathematikRuprecht-Karls-Universität HeidelbergHeidelbergGermany
  6. 6., FB 4 - Department MathematikUniversität TrierTrierGermany
  7. 7.Fakultät für Mathematik, M1, Lehrstuhl für Mathematische OptimierungTechnische Universität MünchenGarching bei MünchenGermany
  8. 8., Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany

Bibliographic information