Stochastic Optimization Methods

✍ Scribed by Univ. Professor Dr. sc. math. Kurt Marti (auth.)

• Publisher: Springer Berlin Heidelberg
• Year: 2005
• Tongue: English
• Leaves: 316
• Category: Library

✦ Synopsis

Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.

✦ Table of Contents

Decision/Control Under Stochastic Uncertainty....Pages 3-8
Deterministic Substitute Problems in Optimal Decision Under Stochastic Uncertainty....Pages 9-42
Differentiation Methods for Probability and Risk Functions....Pages 45-93
Deterministic Descent Directions and Efficient Points....Pages 97-126
RSM-Based Stochastic Gradient Procedures....Pages 129-176
Stochastic Approximation Methods with Changing Error Variances....Pages 177-249
Approximation of the Probability of Failure/Survival in Plastic Structural Analysis and Optimal Plastic Design....Pages 253-271

✦ Subjects

Operations Research/Decision Theory; Optimization; Numerical and Computational Methods in Engineering