## A Direct Method for Parabolic PDE Constrained Optimization ProblemsAndreas 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. |

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### Contents

1 | |

Part I Theoretical foundations | 9 |

Part II Numerical methods | 30 |

Part III Applications and numerical results | 161 |

16 Conclusions and future work | 199 |

201 | |

### Other editions - View all

A Direct Method for Parabolic PDE Constrained Optimization Problems Andreas Potschka No preview available - 2013 |

A Direct Method for Parabolic Pde Constrained Optimization Problems Andreas Potschka No preview available - 2013 |

### Common terms and phrases

Active Set methods Advances in Numerical algorithm approach asymptotic Bock bound Chapter chemotaxis Cholesky decomposition classical Newton-Picard coarse grid column compute Constrained Optimization Problems constraint convergence CPLEX define denote derivatives Deuflhard 44 Differential Equations dimensional dual variables efficient eigenvalues error evaluation Fachmedien Wiesbaden 2014 Figure finite GINKO global GNU Octave heat equation Hessian approximation Hessian matrix homotopy inexact SQP method initial value Interior Point methods invertible iteration Jacobian Lemma linear linear algebra LISA LISA-Newton method Method for Parabolic MUSCOP natural level function Newton method Newton-Picard Newton-Picard preconditioner Newton-type methods nonlinear null space obtain OCPs optimal control Parabolic PDE Constrained PASM PDE Constrained Optimization PDE OCPs Potschka preconditioner primal primal-dual Proof rpasm satisfy Section shooting interval Simplified Newton solution solve solver space spatial discretization Springer Fachmedien Wiesbaden strategy structure subproblems subspace Theorem thesis tion yields