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POD a-posteriori error estimates for linear-quadratic optimal control problems

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Abstract

The main focus of this paper is on an a-posteriori analysis for the method of proper orthogonal decomposition (POD) applied to optimal control problems governed by parabolic and elliptic PDEs. Based on a perturbation method it is deduced how far the suboptimal control, computed on the basis of the POD model, is from the (unknown) exact one. Numerical examples illustrate the realization of the proposed approach for linear-quadratic problems governed by parabolic and elliptic partial differential equations.

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Authors and Affiliations

  1. Institute of Mathematics, Faculty II—Mathematics and Natural Sciences, Berlin University of Technology, Strasse des 17. Juni 136, 10623, Berlin, Germany

    F. Tröltzsch

  2. Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010, Graz, Austria

    S. Volkwein

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  1. F. Tröltzsch
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  2. S. Volkwein
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Correspondence to S. Volkwein.

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Tröltzsch, F., Volkwein, S. POD a-posteriori error estimates for linear-quadratic optimal control problems. Comput Optim Appl 44, 83–115 (2009). https://doi.org/10.1007/s10589-008-9224-3

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  • DOI: https://doi.org/10.1007/s10589-008-9224-3

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