Stochastic Optimization Methods - Hardcover

Marti, Kurt

Hardcover

ISBN 10: 3540222723 ISBN 13: 9783540222729

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2004

Synopsis

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.

About this title

Review

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. a ] 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 authora (TM)s intensive research in this field within the last 25 years. a ] The monograph contains many interesting details, results and explanations in semi-stochastic approximation methods and descent algorithms for stochastic optimization problems. a ] 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. a ] The most important feature of this book is that it has a collection of solution techniques used in optimization methods. a ] More of these applications on different disciplines such as economics a ] 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)

From the Back Cover

Optimization problems arising in practice involve random model parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive 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.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 2004
• Language: English
• ISBN 10: 3540222723
• ISBN 13: 9783540222729
• Binding: Hardcover
• Number of pages: 327