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On an inexact gradient method using Proper Orthogonal Decomposition for parabolic optimal control problems

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Abstract

This paper is devoted to a numerical solution technique for linear quadratic parabolic optimal control problems using the model order reduction technique of Proper Orthogonal Decomposition (POD). The proposed technique is an inexact gradient descent method where the step size is determined with a line-search algorithm evaluating the state and adjoint equations with POD. The gradient is evaluated with a Finite Element method which allows for a recently developed a posteriori error estimation technique to rate the error in the control. The method is compared to another algorithm presented by Tröltzsch and Volkwein (Comput. Optim. Appl. 42(1):43–63 2009).

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Acknowledgements

This work has been supported by DFG SPP1253 HE5386/7-1, HE5386/8-1, DAAD 50756459, 50727872 and IGF 16.557N

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Authors and Affiliations

  1. RWTH Aachen University, Templergraben 55, 52056, Aachen, Germany

    Christian Jörres & Michael Herty

  2. Chair for Applied Mathematics and Numerical Simulation, Niederrhein University of Applied Sciences, Reinarzstr. 49, 47805, Krefeld, Germany

    Georg Vossen

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  1. Christian Jörres
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  2. Georg Vossen
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Correspondence to Christian Jörres.

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Jörres, C., Vossen, G. & Herty, M. On an inexact gradient method using Proper Orthogonal Decomposition for parabolic optimal control problems. Comput Optim Appl 55, 459–468 (2013). https://doi.org/10.1007/s10589-013-9533-z

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