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A Direct Method for Parabolic PDE Constrained Optimization Problems

ANM: DRCT MTHD PARABOLIC PDE CNSTRND OPTMZTN PROBLEMS

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B2B & B2C

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.

POST SECONDARY FOUR YEAR

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Front Cover.
Editorial Board.
Title Page.
Copyright Page.
Acknowledgments.
Abstract.
Contents.
List of Acronyms.
Introduction.
1: Theoretical Foundations.
2: Problem Formulation.
3: Direct Optimization: Problem Discretization.
4: Elements of Optimization Theory.
5: Numerical Methods.
6: Inexact Sequential Quadratic Programming.
7: Newton-Picard Preconditioners.
8: One-Shot One-Step Methods and Their Limitations.
9: Condensing.
10: A Parametric Active Set Method for QP Solution.
11: Automatic Derivative Generation.
12: The Software Package MUSCOP.
13: Applications and Numerical Results.
14: Linear Boundary Control for the Periodic 2D Heat Equation.
15: Nonlinear Boundary Control of the Periodic 1D Heat Equation.
16: Optimal Control for a Bacterial Chemotaxis System.
17: Optimal Control of a Simulated Moving Bed Process.
18: Conclusions and Future Work.
Bibliography.

A Direct Method for Parabolic PDE Constrained Optimization Problems.css-1p8rvzy{position:absolute;padding-left:8px;}

A Direct Method for Parabolic PDE Constrained Optimization Problems