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Stochastic Optimization Methods

Authors: Marti, Kurt

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  • ISBN 978-3-540-26848-2
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About this book

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.

Reviews

From the reviews:

"The aim of the present book is to provide analytical and numerical tools, together with their mathematical foundations, for the approximate computation of robust optimal decisions/designs as needed in concrete engineering/economic applications. … The book is well written and the presentation is rigourous and self-contained." (I.M. Stancu-Minasian, Zentralblatt MATH, Vol. 1059 (10), 2005)

"The monograph by K. Marti investigates the stochastic optimization approach and presents the deep results of the author’s intensive research in this field within the last 25 years. … The monograph contains many interesting details, results and explanations in semi-stochastic approximation methods and descent algorithms for stochastic optimization problems. … Readers interested in these topics will definitely benefit from the monograph." (Stephan Dempe, OR News, 2006)

"The book basically goes through the control problem under stochastic uncertainity, which is drawn from the application of engineering and operational research problems. … The most important feature of this book is that it has a collection of solution techniques used in optimization methods. … More of these applications on different disciplines such as economics … made the book accessible for a wider audience and led to a generally more interesting book." (S. Gazioglu, Journal of the Operational Research Society, Vol. 58 (6), 2007)


Table of contents (7 chapters)

Table of contents (7 chapters)
  • Decision/Control Under Stochastic Uncertainty

    Pages 3-8

  • Deterministic Substitute Problems in Optimal Decision Under Stochastic Uncertainty

    Pages 9-42

  • Differentiation Methods for Probability and Risk Functions

    Pages 45-93

  • Deterministic Descent Directions and Efficient Points

    Pages 97-126

  • RSM-Based Stochastic Gradient Procedures

    Pages 129-176

Buy this book

eBook 88,80 €
price for Spain (gross)
  • ISBN 978-3-540-26848-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Optimization Methods
Authors
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-26848-2
DOI
10.1007/b138181
Edition Number
1
Number of Pages
XIII, 314
Number of Illustrations
14 b/w illustrations
Topics