*** Proof of Product ***
Exploring the Essential Features of “Kurth Marti – Stochastic Optimization Methods (2nd Ed.)”
Authors: Kurt Marti
Many illustrations/several examples/applications to concrete problems from engineering and operations research,
as e.g. quality engineering, robust design/many references to stochastic optimization, stochastic programming and its application to engineering, operations research and economics/presentation of the material from the practical viewpoint
Table of contents (7 chapters)
Front Matter
Pages i-xiii
PDF
Basic Stochastic Optimization Methods
- Decision/Control Under Stochastic Uncertainty
Pages 3-8 - Deterministic Substitute Problems in Optimal Decision Under Stochastic Uncertainty
Pages 9-39
Differentiation Methods
- Differentiation Methods for Probability and Risk Functions
Pages 43-92
Deterministic Descent Directions
- Deterministic Descent Directions and Efficient Points
Pages 95-125
Semi-Stochastic Approximation Methods
- RSM-Based Stochastic Gradient Procedures
Pages 129-176 - Stochastic Approximation Methods with Changing Error Variances
Pages 177-249
Reliability Analysis of Structures/Systems
- Computation of Probabilities of Survival/Failure by Means of Piecewise Linearization of the State Function
Pages 253-297
Back Matter
Pages 301-340
About this book
Optimization problems arising in practice involve random model parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insenistive 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.
Authors and Affiliations
Department of Aerospace Engineering and Technology, University Munich, 85577, Germany
Kurt Marti
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.
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