Trends in PDE constrained optimization
Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored as...
Gespeichert in:
| Weitere Verfasser: | , , , , , , , |
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| Dokumenttyp: | Edited Volume |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham Heidelberg
Birkhäuser
[2014]
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| Schriftenreihe: | International series of numerical mathematics
volume 165 |
| In: |
International series of numerical mathematics (volume 165)
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| Volumes / Articles: | Show Volumes / Articles. |
| Schlagworte: | |
| Online-Zugang: | Aggregator, Volltext: https://ebookcentral.proquest.com/lib/kxp/detail.action?docID=1967902 Verlag, Volltext: http://gbv.eblib.com/patron/FullRecord.aspx?p=1967902 Verlag, Zentralblatt MATH, Inhaltstext: https://zbmath.org/?q=an:1306.49001 
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| Verfasserangaben: | Günter Leugering, Peter Benner, Sebastain Engell, Andreas Griewank, Helmut Harbrecht, Michael Hinze, Rolf Rannacher, Stefan Ulbrich (editors) |
Inhaltsangabe:
- Contents; Contributors; Introduction; 1 Constrained Optimization, Identification and Control; 2 Shape and Topology Optimization; 3 Adaptivity and Model Reduction; 4 Discretization: Concepts and Analysis; 5 Applications; Part I Constrained Optimization, Identification and Control; Introduction to Part I Constrained Optimization, Identification and Control; Optimal Control of Allen-Cahn Systems; 1 Introduction and Problem Formulation; 2 Existence Theory and First-Order Optimality Conditions; 2.1 Smooth ; 2.2 Obstacle Potential; 2.2.1 Penalization Approach Without Distributed Control
- 2.2.2 Relaxation Approach with Distributed Control and Without Elasticity3 Numerics; 3.1 Smooth Potential; 3.1.1 Newton's Method; 3.1.2 Discretization and Error Estimation; 3.1.3 Numerical Results; 3.2 Obstacle Potential; References; Optimal Control of Elastoplastic Processes: Analysis, Algorithms, Numerical Analysis and Applications; 1 Introduction; 2 Optimal Control Problems in Small-Strain Static Elastoplasticity; 2.1 Notation and Standing Assumptions; 2.1.1 Variables; 2.1.2 Function Spaces; 2.1.3 Yield Function and Admissible Stresses; 2.1.4 Operators and Forms
- 2.2 The Forward Problem and Its Regularization2.3 The Quasi-static Forward Problem; 2.4 An Optimal Control Problem; 3 Optimality Conditions; 4 Numerical Results; 5 Further Results of the Project and Ongoing Work; References; One-Shot Approaches to Design Optimzation; 1 From Simulation to Optimization; 2 Problem Formulation and Optimality Conditions; 2.1 The Fixed-Point Solver Paradigm; 2.2 Problem and Solver Characteristics; 3 Jacobi and Seidel One-Shot; 3.1 Jacobi One-Shot Iteration; 3.2 Augmented Lagrangian Preconditioning; 3.3 Seidel One-Shot Approach; 3.4 Finite Termination on QPs
- 3.5 Asymptotic Convergence Rate4 Other Approaches; 5 Numerical Results; 6 Summary and Outlook; References; Optimal Design with Bounded Retardation for Problems with Non-separable Adjoints; 1 Introduction; 2 Exact Quantification of Retardation; 3 Application in Marine Science; 3.1 Calibration of a Box Model of the North Atlantic Circulation; 3.2 Calibration of a 3-D Marine Ecosystem Model; 4 One-Shot in Function Spaces; 5 Adaptive Sequencing of Primal, Adjoint and Control Updates; 6 Application in Aerodynamic Shape Optimization; 7 One-Shot Optimization with Unsteady PDE Constraints; Conclusion
- ReferencesOn a Fully Adaptive SQP Method for PDAE-Constrained Optimal Control Problems with Control and State Constraints; 1 Introduction; 2 Adaptive Multilevel Generalized SQP Method; 2.1 Moreau-Yosida Regularization; 2.2 Multilevel Generalized Adaptive SQP Algorithm; 2.3 Multilevel SQP Method for State Constraints; 2.3.1 Refinement Conditions; 2.3.2 Penalty Parameter Update; 2.3.3 Algorithm; 2.4 Auxiliary Lemmas; 2.5 Main Convergence Results; 3 Numerical Experiments; 3.1 Optimization Environment; 3.2 Glass Cooling Problem; 3.3 Thermistor Problem; Conclusions; References
- Optimal Control of Nonlinear Hyperbolic Conservation Laws with Switching