Optimization under uncertainty : robust parameter estimation with erroneous measurements and uncertain model coefficients
In particular in the last decade, optimization under uncertainty has engaged attention in the mathematical community and beyond. When trying to model the behavior of real-world processes mathematically, this behavior is often not fully understood. Uncertainty may concern the involved species of biol...
Reine und Angewandte Mathematik
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|Zusammenfassung:||In particular in the last decade, optimization under uncertainty has engaged attention in the mathematical community and beyond. When trying to model the behavior of real-world processes mathematically, this behavior is often not fully understood. Uncertainty may concern the involved species of biological or chemical reactions, the kind of reactions taking place, and the numerical values of model coefficients. But also experimental measurements, which form the basis for the determination of the model parameters, contain unavoidable errors. In order to judge the validity and reliability of the numerical results of simulations and model predictions, the inherent uncertainties have at least to be quantified. But it would be even better to incorporate these uncertainties in the mathematical computations from the beginning to derive solutions that are insensitive with respect to such perturbations. The present dissertation starts with an introductory chapter that examines the background of the thesis, in particular the distinct sources of uncertainties and errors in mathematical models. The structure of the remaining part of the thesis is guided by the different types of uncertainties that may be relevant in numerical optimization. Part I of the dissertation deals with measurement errors in the experimental data and part II of the dissertation treats the case of uncertainties in the model coefficients. Part III of the dissertation, finally, contains numerical examples that illustrate the theoretical considerations of the previous chapters.|