Stochastic Optimization Methods: Applications in Engineering and Operations Research

by Kurt Marti

Overview

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 shastic 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 shastic 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, shastic approximation and gradient procedures and differentiation formulas for probabilities and expectations.

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

Product Details

ISBN-13:	9783662500125
Publisher:	Springer Berlin Heidelberg
Publication date:	03/06/2016
Edition description:	3rd ed. 2015
Pages:	368
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

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 “Shastic Optimization” and has been Chairman of the GAMM-Special Interest Group “Applied Shastics 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.

Table of Contents

Shastic Optimization Methods.- Optimal Control Under Shastic Uncertainty.- Shastic Optimal Open-Loop Feedback Control.- Adaptive Optimal Shastic Trajectory Planning and Control (AOSTPC).- Optimal Design of Regulators.- Expected Total Cost Minimum Design of Plane Frames.- Shastic Structural Optimization with Quadratic Loss Functions.- Maximum Entropy Techniques.

Editorial Reviews

The considered book presents a mathematical analysis of the shastic models of important applied optimization problems. … presents detailed methods to solve these problems, rigorously proves their properties, and uses examples to illustrate the proposed methods. This book would be particularly beneficial to mathematicians working in the field of shastic control and mechanical design.” (Antanas Zilinskas, Interfaces, Vol. 45 (6), 2015)

From the Publisher