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Stochastic Optimization Methods

Stochastic Optimization Methods by Kurt Marti
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Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.

Springer Berlin Heidelberg; December 2005
325 pages; ISBN 9783540268482
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Title: Stochastic Optimization Methods
Author: Kurt Marti
 
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ISBNs
3540268480
9783540222729
9783540268482