Stochastic Optimization Methods

Author: Dr. Kurt Marti

Publisher: Springer Berlin Heidelberg

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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.

Frontmatter

Basic Stochastic Optimization Methods

1. Decision/Control Under Stochastic Uncertainty

2. Deterministic Substitute Problems in Optimal Decision Under Stochastic Uncertainty

Differentiation Methods

3. Differentiation Methods for Probability and Risk Functions

Deterministic Descent Directions

4. Deterministic Descent Directions and Efficient Points

Semi-Stochastic Approximation Methods

5. RSM-Based Stochastic Gradient Procedures

6. Stochastic Approximation Methods with Changing Error Variances

Reliability Analysis of Structures/Systems

7. Computation of Probabilities of Survival/Failure by Means of Piecewise Linearization of the State Function

Backmatter

Title: Stochastic Optimization Methods
Author: Dr. Kurt Marti
Publisher: Springer Berlin Heidelberg
Electronic ISBN: 978-3-540-79458-5
Print ISBN: 978-3-540-79457-8
DOI: https://doi.org/10.1007/978-3-540-79458-5

Springer Professional