A Direct Method for Parabolic PDE Constrained Optimization Problems

1. Front Matter

   Pages I-XIV

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2. Introduction

   • Andreas Potschka

   Pages 1-8

3. Theoretical foundations

   1. Front Matter

      Pages 9-9

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   2. Problem formulation

      • Andreas Potschka

      Pages 11-17

   3. Direct Optimization: Problem discretization

      • Andreas Potschka

      Pages 19-26

   4. Elements of optimization theory

      • Andreas Potschka

      Pages 27-29

4. Numerical methods

   1. Front Matter

      Pages 31-31

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   2. Inexact Sequential Quadratic Programming

      • Andreas Potschka

      Pages 33-73

   3. Newton-Picard preconditioners

      • Andreas Potschka

      Pages 75-98

   4. One-shot one-step methods and their limitations

      • Andreas Potschka

      Pages 99-110

   5. Condensing

      • Andreas Potschka

      Pages 111-122

   6. A Parametric Active Set method for QP solution

      • Andreas Potschka

      Pages 123-144

   7. Automatic derivative generation

      • Andreas Potschka

      Pages 145-151

   8. The software package MUSCOP

      • Andreas Potschka

      Pages 153-160

5. Applications and numerical results

   1. Front Matter

      Pages 161-161

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   2. Linear boundary control for the periodic 2D heat equation

      • Andreas Potschka

      Pages 163-170

   3. Nonlinear boundary control of the periodic 1D heat equation

      • Andreas Potschka

      Pages 171-179

   4. Optimal control for a bacterial chemotaxis system

      • Andreas Potschka

      Pages 181-186

   5. Optimal control of a Simulated Moving Bed process

      • Andreas Potschka

      Pages 187-197

6. Back Matter

   Pages 199-216

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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.

• nonlinear optimization
• nonlinear partial differential equations
• preconditioning
• quadratic optimization
• biochemical engineering
• partial differential equations

From the book reviews:

“The thesis is well written and organized, structured in three parts: theoretical foundations, numerical methods, and applications and numerical results. The target groups are researches and students in the fields of mathematics, information systems and scientific computing as well as users confronted with PDE constrained optimization problems.” (Ctirad Matonoha, zbMATH, Vol. 1293, 2014)

• Heidelberg, Germany

  Andreas Potschka

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.

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