Constrained Optimization and Optimal Control for Partial Differential Equations

1. Front Matter

   Pages i-xi

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2. Constrained Optimization, Identification and Control

   1. Front Matter

      Pages 1-3

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   2. Stabilization of Incompressible Flow Problems by Riccati-based Feedback

      • Eberhard Bänsch, Peter Benner

      Pages 5-20

   3. Allen-Cahn and Cahn-Hilliard Variational Inequalities Solved with Optimization Techniques

      • Luise Blank, Martin Butz, Harald Garcke, Lavinia Sarbu, Vanessa Styles

      Pages 21-35

   4. On the Connection Between Forward and Optimization Problem in One-shot One-step Methods

      • Hans Georg Bock, Andreas Potschka, Sebastian Sager, Johannes P. Schlöder

      Pages 37-49

   5. Generalized Multilevel SQP-methods for PDAE-constrained Optimization Based on Space-Time Adaptive PDAE Solvers

      • Debora Clever, Jens Lang, Stefan Ulbrich, Carsten Ziems

      Pages 51-74

   6. Projection Based Model Reduction for Optimal Design of the Time-dependent Stokes System

      • Thomas Franke, Ronald H. W. Hoppe, Christopher Linsenmann, Achim Wixforth

      Pages 75-98

   7. Automated Extension of Fixed Point PDE Solvers for Optimal Design with Bounded Retardation

      • Nicolas Gauger, Andreas Griewank, Adel Hamdi, Claudia Kratzenstein, Emre Özkaya, Thomas Slawig

      Pages 99-122

   8. Well-posedness of Networked Hyperbolic Systems of Balance Laws

      • Martin Gugat, Michael Herty, Axel Klar, Günther Leugering, Veronika Schleper

      Pages 123-146

   9. A Space-Time Multigrid Method for Optimal Flow Control

      • Michael Hinze, Michael Köster, Stefan Turek

      Pages 147-170

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

       • Michael Hinze, Morten Vierling

       Pages 171-182

   11. Structure Exploiting Adjoints for Finite Element Discretizations

       • Denise Holfeld, Philipp Stumm, Andrea Walther

       Pages 183-196

   12. Computing Covariance Matrices for Constrained Nonlinear Large Scale Parameter Estimation Problems Using Krylov Subspace Methods

       • Ekaterina Kostina, Olga Kostyukova

       Pages 197-212

3. Shape and Topology Optimization

   1. Front Matter

      Pages 213-214

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   2. On Shape Optimization with Stochastic Loadings

      • Pradeep Atwal, Sergio Conti, Benedict Geihe, Martin Pach, Martin Rumpf, Rüdiger Schultz

      Pages 215-243

   3. Phase-field Approaches to Structural Topology Optimization

      • Luise Blank, Harald Garcke, Lavinia Sarbu, Tarin Srisupattarawanit, Vanessa Styles, Axel Voigt

      Pages 245-256

   4. Advanced Numerical Methods for PDE Constrained Optimization with Application to Optimal Design in Navier Stokes Flow

      • Christian Brandenburg, Florian Lindemann, Michael Ulbrich, Stefan Ulbrich

      Pages 257-275

   5. Shape Optimization for Free Boundary Problems – Analysis and Numerics

      • Karsten Eppler, Helmut Harbrecht

      Pages 277-288

   6. Non-parametric Aerodynamic Shape Optimization

      • Nicolas Gauger, Caslav Ilic, Stephan Schmidt, Volker Schulz

      Pages 289-300

4. Model Reduction

   1. Front Matter

      Pages 301-302

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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.

• partial differential equations

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

  Günter Leugering

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

  Sebastian Engell

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

  Andreas Griewank

• , Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany

  Michael Hinze

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

  Rolf Rannacher

• , FB 4 - Department Mathematik, Universität Trier, Trier, Germany

  Volker Schulz

• Fakultät für Mathematik, M1, Lehrstuhl für Mathematische Optimierung, Technische Universität München, Garching bei München, Germany

  Michael Ulbrich

• , Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany

  Stefan Ulbrich

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