A Direct Method for Parabolic PDE Constrained Optimization Problems

  • Andreas Potschka
Part of the Advances in Numerical Mathematics book series (ANUM)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Andreas Potschka
    Pages 1-8
  3. Theoretical foundations

    1. Front Matter
      Pages 9-9
    2. Andreas Potschka
      Pages 11-17
    3. Andreas Potschka
      Pages 19-26
    4. Andreas Potschka
      Pages 27-29
  4. Numerical methods

    1. Front Matter
      Pages 31-31
    2. Andreas Potschka
      Pages 33-73
    3. Andreas Potschka
      Pages 75-98
    4. Andreas Potschka
      Pages 99-110
    5. Andreas Potschka
      Pages 111-122
    6. Andreas Potschka
      Pages 123-144
    7. Andreas Potschka
      Pages 145-151
    8. Andreas Potschka
      Pages 153-160
  5. Applications and numerical results

    1. Front Matter
      Pages 161-161
    2. Andreas Potschka
      Pages 181-186
    3. Andreas Potschka
      Pages 187-197
  6. Back Matter
    Pages 199-216

About this book

Introduction

Andreas Potschka discusses a direct multiple shooting method for dynamic optimization problems constrained by nonlinear, possibly time-periodic, parabolic partial differential equations. In contrast to indirect methods, this approach automatically computes adjoint derivatives without requiring the user to formulate adjoint equations, which can be time-consuming and error-prone. The author describes and analyzes in detail a globalized inexact Sequential Quadratic Programming method that exploits the mathematical structures of this approach and problem class for fast numerical performance. The book features applications, including results for a real-world chemical engineering separation problem.

 

Contents

·         Parabolic PDE Constrained Optimization Problems

·         Two-Grid Newton-Picard Inexact SQP

·         Structure Exploiting Solution of QPs

·         Applications and Numerical Results

 

 

 

Target Groups

·         Researchers and students in the fields of mathematics, information systems, and scientific computing

·         Users with PDE constrained optimization problems, in particular in (bio-)chemical engineering

 

The Author

Dr. Andreas Potschka is a postdoctoral researcher in the Simulation and Optimization group of Prof. Dr. Dres. h. c. Hans Georg Bock at the Interdisciplinary Center for Scientific Computing, Heidelberg University. He is the head of the research group Model-Based Optimizing Control.

Keywords

nonlinear optimization nonlinear partial differential equations preconditioning quadratic optimization

Authors and affiliations

  • Andreas Potschka
    • 1
  1. 1.HeidelbergGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-658-04476-3
  • Copyright Information Springer Fachmedien Wiesbaden 2014
  • Publisher Name Springer Spektrum, Wiesbaden
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-658-04475-6
  • Online ISBN 978-3-658-04476-3
  • Series Print ISSN 1616-2994
  • About this book