Stochastic Optimization Methods
Applications in Engineering and Operations Research
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Beschreibung
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.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.
Features optimization problems that in practice involve random model parameters Provides applications from the fields of robust optimal control / design in case of stochastic uncertainty Includes numerous references to stochastic optimization, stochastic programming and its applications to engineering, operations research and economics Includes supplementary material: sn.pub/extras
Autor*in
Kurt Marti
Themen in »Stochastic Optimization Methods«
calculus model optimization problems regression response surface methodology stochastic approximation stochastic optimization
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“The considered book presents a mathematical analysis of the stochastic 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 stochastic control and mechanical design.” (Antanas Zilinskas, Interfaces, Vol. 45 (6), 2015)
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