TY  - DATA
AU  - Marti, Kurt.
TI  - Stochastic Optimization Methods
SN  - 9783540794585
U1  - 658.403 23
PY  - 2008///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg, Imprint: Springer
KW  - Operations research
KW  - Mathematical optimization
KW  - Engineering
KW  - Computational intelligence
KW  - Operations Research and Decision Theory
KW  - Optimization
KW  - Technology and Engineering
KW  - Computational Intelligence
N1  - Basic Stochastic Optimization Methods -- Decision/Control Under Stochastic Uncertainty -- Deterministic Substitute Problems in Optimal Decision Under Stochastic Uncertainty -- Differentiation Methods -- Differentiation Methods for Probability and Risk Functions -- Deterministic Descent Directions -- Deterministic Descent Directions and Efficient Points -- Semi-Stochastic Approximation Methods -- RSM-Based Stochastic Gradient Procedures -- Stochastic Approximation Methods with Changing Error Variances -- Reliability Analysis of Structures/Systems -- Computation of Probabilities of Survival/Failure by Means of Piecewise Linearization of the State Function
N2  - 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
UR  - https://doi.org/10.1007/978-3-540-79458-5
ER  -