Stochastic Optimization MethodsMarti, Kurt

2nd ed., 2008, XIII, 340 p. 23 illus., Hardcover
ISBN: 978-3-540-79457-8








About this book
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.

Written for:
Researchers
Keywords:

• Optimization
• Optimization Problems
• Stochastic Approximation
• Stochastic Optimization

Table of contents

Part I Basic Stochastic Optimization Methods: Decision/Control Under Stochastic Uncertainty.- Deterministic substitute Problems in Optimal Decision.- Under Stochastic Uncertainty.-

Part II Differentiation Methods: Differentiation Methods for Probability and Risk Functions.-

Part III Deterministic Descent Directions: Deterministic Descent Directions and Efficient Points.-

Part IV Semi-Stochastic Approximation Methods: RSM–Based Stochastic Gradient Procedures.- Stochastic Approximation Methods with Changing Error Variances.- Part V Reliability Analysis of Structures/Systems: Computation of probabilities.-

Part VI Appendix: Sequences, Series and Products.- Convergence Theorems for Stochastic Sequences.- Tools from Matrix Calculus.