Trends in PDE Constrained Optimization

1. Front Matter

   Pages i-xiv

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2. Introduction

   • 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

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   2. Introduction to Part I Constrained Optimization, Identification and Control

      • Stefan Ulbrich, Andreas Griewank

      Pages 7-9

   3. Optimal Control of Allen-Cahn Systems

      • Luise Blank, M. Hassan Farshbaf-Shaker, Claudia Hecht, Josef Michl, Christoph Rupprecht

      Pages 11-26

   4. Optimal Control of Elastoplastic Processes: Analysis, Algorithms, Numerical Analysis and Applications

      • Roland Herzog, Christian Meyer, Gerd Wachsmuth

      Pages 27-41

   5. One-Shot Approaches to Design Optimzation

      • Torsten Bosse, Nicolas R. Gauger, Andreas Griewank, Stefanie Günther, Volker Schulz

      Pages 43-66

   6. Optimal Design with Bounded Retardation for Problems with Non-separable Adjoints

      • Torsten Bosse, Nicolas R. Gauger, Andreas Griewank, Stefanie Günther, Lena Kaland, Claudia Kratzenstein et al.

      Pages 67-84

   7. On a Fully Adaptive SQP Method for PDAE-Constrained Optimal Control Problems with Control and State Constraints

      • Stefanie Bott, Debora Clever, Jens Lang, Stefan Ulbrich, Jan Carsten Ziems, Dirk Schröder

      Pages 85-108

   8. Optimal Control of Nonlinear Hyperbolic Conservation Laws with Switching

      • Sebastian Pfaff, Stefan Ulbrich, Günter Leugering

      Pages 109-131

   9. Elliptic Mathematical Programs with Equilibrium Constraints in Function Space: Optimality Conditions and Numerical Realization

      • Michael Hintermüller, Antoine Laurain, Caroline Löbhard, Carlos N. Rautenberg, Thomas M. Surowiec

      Pages 133-153

   10. Models and Optimal Control in Freezing and Thawing of Living Cells and Tissues

       • Karl-Heinz Hoffmann, Nikolai D. Botkin, Varvara L. Turova

       Pages 155-172

   11. Optimal Control-Based Feedback Stabilization of Multi-field Flow Problems

       • Eberhard Bänsch, Peter Benner, Jens Saak, Heiko K. Weichelt

       Pages 173-188

4. Shape and Topology Optimization

   1. Front Matter

      Pages 189-189

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   2. Introduction to Part II Shape and Topology Optimization

      • Helmut Harbrecht

      Pages 191-191

   3. Two-Stage Stochastic Optimization Meets Two-Scale Simulation

      • Sergio Conti, Benedict Geihe, Martin Rumpf, Rüdiger Schultz

      Pages 193-211

   4. On Shape Optimization with Parabolic State Equation

      • Helmut Harbrecht, Johannes Tausch

      Pages 213-229

   5. Multi-material Phase Field Approach to Structural Topology Optimization

      • 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

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   2. Introduction to Part III Adaptivity and Model Reduction

      • Peter Benner, Rolf Rannacher

      Pages 249-250

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

• Department Mathematik, Universität Erlangen-Nürnberg, Erlangen, Germany

  Günter Leugering

• Institut für Dynamik komplexer technisch, Max-Planck-Institut, Magdeburg, Germany

  Peter Benner

• Fakultät Bio- und Chemieingenieurwesen, Technische Universität Dortmund, Dortmund, Germany

  Sebastian Engell

• Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Germany

  Andreas Griewank

• Mathematisches Institut, Universität Basel, Basel, Switzerland

  Helmut Harbrecht

• Fachbereich Mathematik Optimierung und Approximation, Universität Hamburg, Hamburg, Germany

  Michael Hinze

• Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

  Rolf Rannacher

• Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany

  Stefan Ulbrich

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