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...
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| Weitere Verfasser: | , , , , , , , |
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| Dokumenttyp: | Sammelband |
| 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) |
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| 245 | 0 | 0 | |a Trends in PDE constrained optimization |c Günter Leugering, Peter Benner, Sebastain Engell, Andreas Griewank, Helmut Harbrecht, Michael Hinze, Rolf Rannacher, Stefan Ulbrich (editors) |
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| 490 | 1 | |a International series of numerical mathematics |v volume 165 | |
| 500 | |a Description based on publisher supplied metadata and other sources | ||
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a Optimal Control of Nonlinear Hyperbolic Conservation Laws with Switching | |
| 520 | |a 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 part of the Deutsche Forschungsgemeinschaft (DFG) priority program 1253 on "Optimization with Partial Differential Equations" from 2006 to 2013. The investigations were motivated by the fascinating potential applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume, contributions from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics. The book is divided into five sections on "Constrained Optimization, Identification and Control", "Shape and Topology Optimization", "Adaptivity and Model Reduction", "Discretization: Concepts and Analysis" and "Applications". Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview of topics that set sustainable trends for future research. This makes this special volume interesting not only for mathematicians, but also for engineers and for natural and medical scientists working on processes that can be modeled by PDEs. | ||
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