Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematical Modelling: Theory and Applications (MMTA, volume 23)
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About this book
Solving optimization problems subject to constraints given in terms of partial d- ferential equations (PDEs) with additional constraints on the controls and/or states is one of the most challenging problems in the context of industrial, medical and economical applications, where the transition from model-based numerical si- lations to model-based design and optimal control is crucial. For the treatment of such optimization problems the interaction of optimization techniques and num- ical simulation plays a central role. After proper discretization, the number of op- 3 10 timization variables varies between 10 and 10 . It is only very recently that the enormous advances in computing power have made it possible to attack problems of this size. However, in order to accomplish this task it is crucial to utilize and f- ther explore the speci?c mathematical structure of optimization problems with PDE constraints, and to develop new mathematical approaches concerning mathematical analysis, structure exploiting algorithms, and discretization, with a special focus on prototype applications. The present book provides a modern introduction to the rapidly developing ma- ematical ?eld of optimization with PDE constraints. The ?rst chapter introduces to the analytical background and optimality theory for optimization problems with PDEs. Optimization problems with PDE-constraints are posed in in?nite dim- sional spaces. Therefore, functional analytic techniques, function space theory, as well as existence- and uniqueness results for the underlying PDE are essential to study the existence of optimal solutions and to derive optimality conditions.
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Table of contents (4 chapters)
Reviews
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)
Authors and Affiliations
Bibliographic Information
Book Title: Optimization with PDE Constraints
Authors: Michael Hinze, Rene Pinnau, Michael Ulbrich, Stefan Ulbrich
Series Title: Mathematical Modelling: Theory and Applications
DOI: https://doi.org/10.1007/978-1-4020-8839-1
Publisher: Springer Dordrecht
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media B.V. 2009
Hardcover ISBN: 978-1-4020-8838-4Published: 14 November 2008
Softcover ISBN: 978-90-481-8003-5Published: 28 October 2010
eBook ISBN: 978-1-4020-8839-1Published: 16 October 2008
Series ISSN: 1386-2960
Edition Number: 1
Number of Pages: XII, 270
Topics: Calculus of Variations and Optimal Control; Optimization, Analysis, Numerical Analysis