Stochastic Optimization Methods

✍ Scribed by Dr. Kurt Marti (auth.)

• Publisher: Springer Berlin Heidelberg
• Year: 2008
• Tongue: English
• Leaves: 335
• Edition: 2nd ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiii
Decision/Control Under Stochastic Uncertainty....Pages 3-8
Deterministic Substitute Problems in Optimal Decision Under Stochastic Uncertainty....Pages 9-39
Differentiation Methods for Probability and Risk Functions....Pages 43-92
Deterministic Descent Directions and Efficient Points....Pages 95-125
RSM-Based Stochastic Gradient Procedures....Pages 129-176
Stochastic Approximation Methods with Changing Error Variances....Pages 177-249
Computation of Probabilities of Survival/Failure by Means of Piecewise Linearization of the State Function....Pages 253-297
Back Matter....Pages 301-340

✦ Subjects

Operations Research/Decision Theory; Optimization; Computational Intelligence