Optimization with PDE Constraints
Autoren: Hinze, M., Pinnau, R., Ulbrich, M., Ulbrich, S.
Vorschau- Concise functional analytic setting for pde constrained optimization problems
- Modern infinite-dimensional tailored algorithmical framework
- Structure exploiting, problem adapted discrete treatment of pdes and constraints
- Challenging applications
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- Über dieses Buch
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This book presents a modern introduction of pde constrained optimization. It provides a precise functional analytic treatment via optimality conditions and a state-of-the-art, non-smooth algorithmical framework. Furthermore, new structure-exploiting discrete concepts and large scale, practically relevant applications are presented. The main focus is on the algorithmical and numerical treatment of pde constrained optimization problems on the infinite dimensional level. A particular emphasis is on simple constraints, such as pointwise bounds on controls and states. For these practically important situations, tailored Newton- and SQP-type solution algorithms are proposed and a general convergence framework is developed. This is complemented with the numerical analysis of structure-preserving Galerkin schemes for optimization problems with elliptic and parabolic equations. Finally, along with the optimization of semiconductor devices and the optimization of glass cooling processes, two challenging applications of pde constrained optimization are presented. They demonstrate the scope of this emerging research field for future engineering applications.
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From the reviews:
"The book presents a state-of-the-art of optimization problems described by partial differential equations (PDEs) and algorithms for obtaining their solutions. Solving optimization problems with constraints given in terms of PDEs is one of the most challenging problems appearing, e.g., in industry, medical and economical applications. The book consists of four chapters. … This well-written book can be recommended to scientists and graduate students working in the fields of optimal control theory, optimization algorithms and numerical solving of optimization problems described by PDEs." (Wieslaw Kotarski, Zentralblatt MATH, Vol. 1167, 2009)
- Inhaltsverzeichnis (4 Kapitel)
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Analytical Background and Optimality Theory
Seiten 1-95
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Optimization Methods in Banach Spaces
Seiten 97-156
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Discrete Concepts in PDE Constrained Optimization
Seiten 157-232
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Applications
Seiten 233-263
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Inhaltsverzeichnis (4 Kapitel)
- Download Vorwort 1 PDF (70.2 KB)
- Download Probeseiten 2 PDF (596 KB)
- Download Inhaltsverzeichnis PDF (66.5 KB)
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Bibliografische Information
- Bibliographic Information
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- Buchtitel
- Optimization with PDE Constraints
- Autoren
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- Michael Hinze
- Rene Pinnau
- Michael Ulbrich
- Stefan Ulbrich
- Titel der Buchreihe
- Mathematical Modelling: Theory and Applications
- Buchreihen Band
- 23
- Copyright
- 2009
- Verlag
- Springer Netherlands
- Copyright Inhaber
- Springer Science+Business Media B.V.
- eBook ISBN
- 978-1-4020-8839-1
- DOI
- 10.1007/978-1-4020-8839-1
- Hardcover ISBN
- 978-1-4020-8838-4
- Softcover ISBN
- 978-90-481-8003-5
- Buchreihen ISSN
- 1386-2960
- Auflage
- 1
- Seitenzahl
- XII, 270
- Themen
