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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.
Über den Autor / die Autorin
Dr. Kurt Marti ist Professor für Mathematik und Rechneranwendung an der Universität der Bundeswehr in München. Er ist Vorsitzender der IFIP-Arbeitsgruppe zur Stochastischen Optimierung und war Vorsitzender der GAMM-Special-Interest-Group Applied Stochastics and Optimization . Professor Marti ist Verfasser mehrerer deutsch- und englischsprachiger Fachbücher zur angewandten Mathematik und zur Optimierung und hat mehr als 160 Beiträge in wissenschaftlichen Zeitschriften veröffentlicht.
Zusammenfassung
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.
