Optimization with PDE Constraints

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Beschreibung

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.

Zusammenfassung

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: [...]

Inhaltsverzeichnis

Analytical Background and Optimality Theory.- Optimization Methods in Banach Spaces.- Discrete Concepts in PDE Constrained Optimization.- Applications.

Details

Erscheinungsjahr:	2008
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Mathematical Modelling: Theory and Applications
Inhalt:	xii 270 S.
ISBN-13:	9781402088384
ISBN-10:	1402088388
Sprache:	Englisch
Herstellernummer:	12072743
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Hinze, Michael Ulbrich, Stefan Ulbrich, Michael Pinnau, Rene
Hersteller:	Springer Netherland Springer Netherlands Mathematical Modelling: Theory and Applications
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 23 mm
Von/Mit:	Michael Hinze (u. a.)
Erscheinungsdatum:	14.11.2008
Gewicht:	0,646 kg

Artikel-ID: 101770997