Stochastic Optimization Methods
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Beschreibung
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.
Optimization problems arising in practice involve random model parameters. This book features many illustrations, several examples, and applications to concrete problems from engineering and operations research.
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.
Many illustrations/several examples/applications to concrete problems from engineering and operations research, as e.g. quality engineering, robust design/many references to stochastic optimization, stochastic programming and its application to engineering, operations research and economics/presentation of the material from the practical viewpoint
Autor*in
Kurt Marti
Themen in »Stochastic Optimization Methods«
Operations Research Optimization Optimization Methods Optimization Problems Regression Response Surface Methodology Stochastic Approximation Stochastic Optimization calculus model