Stochastic Optimization Methods
(Sprache: Englisch)
Optimization problems arising in practice involve random model parameters. This book features many illustrations, several examples, and applications to concrete problems from engineering and operations research.
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Optimization problems arising in practice involve random model parameters. This book features many illustrations, several examples, and applications to concrete problems from engineering and operations research.
Klappentext zu „Stochastic Optimization Methods “
Optimization problems arising in practice involve random model parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insenistive with respect to random parameter variations, appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into appropriate deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures, differentiation formulas for probabilities and expectations.Inhaltsverzeichnis zu „Stochastic Optimization Methods “
Basic Stochastic Optimization Methods.- Decision/Control Under Stochastic Uncertainty.- Deterministic Substitute Problems in Optimal Decision Under Stochastic Uncertainty.- Differentiation Methods.- Differentiation Methods for Probability and Risk Functions.- Deterministic Descent Directions.- Deterministic Descent Directions and Efficient Points.- Semi-Stochastic Approximation Methods.- RSM-Based Stochastic Gradient Procedures.- Stochastic Approximation Methods with Changing Error Variances.- Reliability Analysis of Structures/Systems.- Computation of Probabilities of Survival/Failure by Means of Piecewise Linearization of the State Function.
Autoren-Porträt von Kurt Marti
Dr. Kurt Marti ist Professor für Mathematik und Rechneranwendung an der Universität der Bundeswehr in München. Er ist Vorsitzender der IFIP-Arbeitsgruppe zur Stochastischen Optimierung und war Vorsitzender der GAMM-Special-Interest-Group Applied Stochastics and Optimization . Professor Marti ist Verfasser mehrerer deutsch- und englischsprachiger Fachbücher zur angewandten Mathematik und zur Optimierung und hat mehr als 160 Beiträge in wissenschaftlichen Zeitschriften veröffentlicht.
Bibliographische Angaben
- Autor: Kurt Marti
- 2008, 2nd ed., 340 Seiten, 23 Schwarz-Weiß-Abbildungen, Maße: 15,5 x 23,5 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3540794573
- ISBN-13: 9783540794578
- Erscheinungsdatum: 04.06.2008
Sprache:
Englisch
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