Repository: Freie Universität Berlin, Math Department

On the treatment of distributed uncertainties in PDE‐constrained optimization

Borzì, Alfio and Schulz, Volker H. and Schillings, Claudia and von Winckel, Gregory (2010) On the treatment of distributed uncertainties in PDE‐constrained optimization. GAMM-Mitteilungen, 33 (2). pp. 230-246.

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Most physical phenomena are significantly affected by uncertainties associated with variations in properties and fluctuations in operating conditions. This has to be reflected also in the design and control of real-application systems. Recent advances in PDE constrained optimization open the possibility of realistic optimization of such systems in the presence of model and data uncertainties. These emerging techniques require only the knowledge of the probability distribution of the perturbations, which is usually available, and provide optimization solutions that are robust with respect to the stochasticity of the application framework. In this paper, some of these methodologies are reviewed. The focus is on PDE constrained optimization frameworks where distributed uncertainties are modeled by random fields and the structures in the underlying optimization problems are exploited in the form of multigrid methods and one-shot methods. Applications are presented, including control problems with uncertain coefficients and erodynamic design under geometric uncertainties (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Deterministic and Stochastic PDEs Group
ID Code:2825
Deposited By: Ulrike Eickers
Deposited On:27 Apr 2022 11:23
Last Modified:27 Apr 2022 11:23

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