Numerical Analysis of Optimality-System POD for Constrained Optimal Control

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2015
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MEHL, Miriam, ed. and others. Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems. Cham [u.a.]: Springer, 2015, pp. 297-317. Lecture Notes in Computational Science and Engineering. 105. ISSN 1439-7358. eISSN 2197-7100. ISBN 978-3-319-22996-6. Available under: doi: 10.1007/978-3-319-22997-3_18
Zusammenfassung

In this work linear-quadratic optimal control problems for parabolic equations with control and state constraints are considered. Utilizing a Lavrentiev regularization we obtain a linear-quadratic optimal control problem with mixed control-state constraints. For the numerical solution a Galerkin discretization is applied utilizing proper orthogonal decomposition (POD). Based on a perturbation method it is determined by a-posteriori error analysis how far the suboptimal control, computed on the basis of the POD method, is from the (unknown) exact one. POD basis updates are computed by optimality-system POD. Numerical examples illustrate the theoretical results for control and state constrained optimal control problems.

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510 Mathematik
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3rd International Workshop on Computational Engineering (CE 2014), 6. Okt. 2014 - 10. Okt. 2014, Stuttgart
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ISO 690GRIMM, Eva, Martin GUBISCH, Stefan VOLKWEIN, 2015. Numerical Analysis of Optimality-System POD for Constrained Optimal Control. 3rd International Workshop on Computational Engineering (CE 2014). Stuttgart, 6. Okt. 2014 - 10. Okt. 2014. In: MEHL, Miriam, ed. and others. Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems. Cham [u.a.]: Springer, 2015, pp. 297-317. Lecture Notes in Computational Science and Engineering. 105. ISSN 1439-7358. eISSN 2197-7100. ISBN 978-3-319-22996-6. Available under: doi: 10.1007/978-3-319-22997-3_18
BibTex
@inproceedings{Grimm2015Numer-32367,
  year={2015},
  doi={10.1007/978-3-319-22997-3_18},
  title={Numerical Analysis of Optimality-System POD for Constrained Optimal Control},
  number={105},
  isbn={978-3-319-22996-6},
  issn={1439-7358},
  publisher={Springer},
  address={Cham [u.a.]},
  series={Lecture Notes in Computational Science and Engineering},
  booktitle={Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems},
  pages={297--317},
  editor={Mehl, Miriam},
  author={Grimm, Eva and Gubisch, Martin and Volkwein, Stefan}
}
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