Stochastic Optimization Methods

by Kurt Marti (Author)

From the Back Cover
This book examines optimization problems that in practice involve random model parameters. It details the computation of robust optimal solutions, i.e., optimal solutions that are insensitive with respect to random parameter variations, where 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 probabilities and expectations involved, the book also shows how to apply approximative solution techniques. 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, and differentiation formulas for probabilities and expectations.

In the third edition, this book further develops stochastic optimization methods. In particular, it now shows how to apply stochastic optimization methods to the approximate solution of important concrete problems arising in engineering, economics and operations research.

About the Author
Dr. Kurt Marti is a full Professor of Engineering Mathematics at the "Federal Armed Forces University of Munich“. He is Chairman of the IFIP-Working Group 7.7 on “Stochastic Optimization” and has been Chairman of the GAMM-Special Interest Group “Applied Stochastics and Optimization”. Professor Marti has published several books, both in German and in English and he is author of more than 160 papers in refereed journals.

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)

Content Level » Research
Keywords » calculus - model - optimization problems - regression - response surface methodology - stochastic approximation - stochastic optimization
Related subjects » Computational Intelligence and Complexity - Mathematics - Operations Research & Decision Theory