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Non-Smooth and Complementarity-Based Distributed Parameter Systems

Simulation and Hierarchical Optimization

  • Book
  • © 2022

Overview

Editors:
  1. Michael Hintermüller

    1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

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  2. Roland Herzog

    1. Institute for Applied Mathematics, University of Heidelberg, Heidelberg, Germany

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  3. Christian Kanzow

    1. Lehrstuhl für Mathematik VII, Julius-Maximilians-Universität Würzburg, Würzburg, Germany

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  4. Michael Ulbrich

    1. Department of Mathematics, Technical University of Munich, Garching b. München, Germany

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  5. Stefan Ulbrich

    1. Fachbereich Mathematik, Technische Universitaet Darmstadt, Darmstadt, Germany

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  • Presents results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems
  • Aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences
  • Considers a wide range of applications, including optimal control of multiphase fluids, image processing, thermoforming, and the formation of rivers and networks

Part of the book series: International Series of Numerical Mathematics (ISNM, volume 172)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-viii
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  2. Error Bounds for Discretized Optimal Transport and Its Reliable Efficient Numerical Solution

    • Sören Bartels, Stephan Hertzog
    Pages 1-20

  3. Numerical Methods for Diagnosis and Therapy Design of Cerebral Palsy by Bilevel Optimal Control of Constrained Biomechanical Multi-Body Systems

    • Hans Georg Bock, Ekaterina Kostina, Marta Sauter, Johannes P. Schlöder, Matthias Schlöder
    Pages 21-41

  4. ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation

    • Stefan Banholzer, Bennet Gebken, Michael Dellnitz, Sebastian Peitz, Stefan Volkwein
    Pages 43-76

  5. Analysis and Solution Methods for Bilevel Optimal Control Problems

    • Stephan Dempe, Felix Harder, Patrick Mehlitz, Gerd Wachsmuth
    Pages 77-99

  6. A Calculus for Non-smooth Shape Optimization with Applications to Geometric Inverse Problems

    • Marc Herrmann, Roland Herzog, Stephan Schmidt, José Vidal-Núñez
    Pages 101-120

  7. Rate-Independent Systems and Their Viscous Regularizations: Analysis, Simulation, and Optimal Control

    • Roland Herzog, Dorothee Knees, Christian Meyer, Michael Sievers, Ailyn Stötzner, Stephanie Thomas
    Pages 121-144

  8. Generalized Nash Equilibrium Problems with Partial Differential Operators: Theory, Algorithms, and Risk Aversion

    • Deborah Gahururu, Michael Hintermüller, Steven-Marian Stengl, Thomas M. Surowiec
    Pages 145-181

  9. Stability and Sensitivity Analysis for Quasi-Variational Inequalities

    • Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg
    Pages 183-210

  10. Simulation and Control of a Nonsmooth Cahn–Hilliard Navier–Stokes System with Variable Fluid Densities

    • Carmen Gräßle, Michael Hintermüller, Michael Hinze, Tobias Keil
    Pages 211-240

  11. Safeguarded Augmented Lagrangian Methods in Banach Spaces

    • Christian Kanzow, Veronika Karl, Daniel Daniel Steck, Wachsmuth
    Pages 241-282

  12. Decomposition and Approximation for PDE-Constrained Mixed-Integer Optimal Control

    • Mirko Hahn, Christian Kirches, Paul Manns, Sebastian Sager, Clemens Zeile
    Pages 283-305

  13. Strong Stationarity for Optimal Control of Variational Inequalities of the Second Kind

    • Constantin Christof, Christian Meyer, Ben Schweizer, Stefan Turek
    Pages 307-327

  14. Optimizing Fracture Propagation Using a Phase-Field Approach

    • Andreas Hehl, Masoumeh Mohammadi, Ira Neitzel, Winnifried Wollner
    Pages 329-351

  15. Algorithms for Optimal Control of Elastic Contact Problems with Finite Strain

    • Anton Schiela, Matthias Stöcklein
    Pages 353-375

  16. Algorithms Based on Abs-Linearization for Non-smooth Optimization with PDE Constraints

    • Olga Weiß, Andrea Walther, Stephan Schmidt
    Pages 377-395

  17. Shape Optimization for Variational Inequalities of Obstacle Type: Regularized and Unregularized Computational Approaches

    • Volker H. Schulz, Kathrin Welker
    Pages 397-420

  18. Extensions of Nash Games in Finite and Infinite Dimensions with Applications

    • Jan Becker, Alexandra Schwartz, Sonja Steffensen, Anna Thünen
    Pages 421-443

  19. Stress-Based Methods for Quasi-Variational Inequalities Associated with Frictional Contact

    • Bernhard Kober, Gerhard Starke, Rolf Krause, Gabriele Rovi
    Pages 445-466

  20. An Inexact Bundle Method and Subgradient Computations for Optimal Control of Deterministic and Stochastic Obstacle Problems

    • Lukas Hertlein, Anne-Therese Rauls, Michael Ulbrich, Stefan Ulbrich
    Pages 467-497
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Keywords

About this book

Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems.  This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences.   Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications.  Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks.


Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.

Editors and Affiliations

  • Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Michael Hintermüller

  • Institute for Applied Mathematics, University of Heidelberg, Heidelberg, Germany

    Roland Herzog

  • Lehrstuhl für Mathematik VII, Julius-Maximilians-Universität Würzburg, Würzburg, Germany

    Christian Kanzow

  • Department of Mathematics, Technical University of Munich, Garching b. München, Germany

    Michael Ulbrich

  • Fachbereich Mathematik, Technische Universitaet Darmstadt, Darmstadt, Germany

    Stefan Ulbrich

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