A Direct Method for Parabolic Pde Constrained Optimization Problems

ISBN-13: 9783658044756 / Angielski / Miękka / 2013 / 216 str.

Andreas Potschka

Opis

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.

Recenzje

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)

Spis treści

Parabolic PDE Constrained Optimization Problems.- Two-Grid Newton-Picard Inexact SQP.- Structure Exploiting Solution of QPs.- Applications and Numerical Results.

O autorze

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.

Blurb

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.