for Kindle Fire, Apple, Android, Nook, Kobo, PC, Mac, BlackBerry ...

New to eBooks.com?

Learn more

Shape Optimization under Uncertainty from a Stochastic Programming Point of View

Shape Optimization under Uncertainty from a Stochastic Programming Point of View by Harald Held
Add to cart
US$ 129.00
(If any tax is payable it will be calculated and shown at checkout.)
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.
Vieweg+Teubner Verlag; May 2010
139 pages; ISBN 9783834893963
Download in secure PDF format
Title: Shape Optimization under Uncertainty from a Stochastic Programming Point of View
Author: Harald Held
 
Buy, download and read Shape Optimization under Uncertainty from a Stochastic Programming Point of View (eBook) by Harald Held today!