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.
Dr. Kurt Marti is a full Professor of Engineering Mathematics at the Federal Armed Forces University of Munich. He is Chairman of the IFIP-Working Group 7.7 on Stochastic Optimization and has been Chairman of the GAMM-Special Interest Group Applied Stochastics and Optimization. Professor Marti has published several books, both in German and in English, and he is author of more than 160 papers in refereed journals.
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.
