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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Wahrscheinlichkeitstheorie & Statistik Shape Optimization under Uncertainty from a Stochastic Programming Point of View
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Shape Optimization under Uncertainty from a Stochastic Programming Point of View
Harald Held (Broschiert, Englisch)
Optischer Zustand
Beschreibung
Optimization problems whose constraints involve partial differential equations (PDEs) are relevant in many areas of technical, industrial, and economic app- cations. At the same time, they pose challenging mathematical research problems in numerical analysis and optimization. The present text is among the ?rst in the research literature addressing stochastic uncertainty in the context of PDE… constrained optimization. The focus is on shape optimization for elastic bodies under stochastic loading. Analogies to ?nite dim- sional two-stage stochastic programming drive the treatment, with shapes taking the role of nonanticipative decisions.The main results concern level set-based s- chastic shape optimization with gradient methods involving shape and topological derivatives. The special structure of the elasticity PDE enables the numerical - lution of stochastic shape optimization problems with an arbitrary number of s- narios without increasing the computational effort signi?cantly. Both risk neutral and risk averse models are investigated. This monograph is based on a doctoral dissertation prepared during 2004-2008 at the Chair of Discrete Mathematics and Optimization in the Department of Ma- ematics of the University of Duisburg-Essen. The work was supported by the Deutsche Forschungsgemeinschaft (DFG) within the Priority Program “Optimi- tion with Partial Differential Equations”. Rüdiger Schultz Acknowledgments I owe a great deal to my supervisors, colleagues, and friends who have always supported, encouraged, andenlightenedmethroughtheirownresearch, comments, and questions. 53,49 €
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Technische Daten
Erscheinungsdatum
28.07.2009
Sprache
Englisch
EAN
9783834809094
Herausgeber
Vieweg & Teubner
Serien- oder Bandtitel
Stochastic Programming
Sonderedition
Nein
Autor
Harald Held
Seitenanzahl
148
Einbandart
Broschiert
Autorenporträt
Dr. Harald Held completed his doctoral thesis at the Department of Mathematics at the University of Duisburg-Essen. He is now a Research Scientist at Siemens AG, Corporate Technology.
Schlagwörter
PDE, Programming, Shape Optimization, Stochastic, Topology, loadings, optimization
Thema-Inhalt
PBT - Wahrscheinlichkeitsrechnung und Statistik
PBWL - Stochastik
PB - Mathematik
Höhe
210 mm
Breite
14.8 cm
Transparenz & Sicherheit
Hersteller: Vieweg+Teubner Verlag, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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