A Direct Method for Parabolic PDE Constrained Optimization Problems, 1st Edition

  • Published By:
  • ISBN-10: 3658044764
  • ISBN-13: 9783658044763
  • DDC: 511.8
  • Grade Level Range: College Freshman - College Senior
  • 216 Pages | eBook
  • Original Copyright 2014 | Published/Released May 2014
  • This publication's content originally published in print form: 2014

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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.

Table of Contents

Front Cover.
Editorial Board.
Title Page.
Copyright Page.
List of Acronyms.
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.