POD-based error control for reduced-order bicriterial PDE-constrained optimization

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Annual Reviews in Control. 2017, 44, pp. 226-237. ISSN 1367-5788. eISSN 1872-9088. Available under: doi: 10.1016/j.arcontrol.2017.09.004
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In the present paper, a bicriterial optimal control problem governed by an abstract evolution problem and bilateral control constraints is considered. To compute Pareto optimal points and the Pareto front numerically, the (Euclidean) reference point method is applied, where many scalar constrained optimization problems have to be solved. For this reason a reduced-order approach based on proper orthogonal decomposition (POD) is utilized. An a-posteriori error analysis ensures a desired accuracy for the Pareto optimal points and for the Pareto front computed by the POD method. Numerical experiments for evolution problems with convection-diffusion illustrate the efficiency of the presented approach.

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ISO 690BANHOLZER, Stefan, Dennis BEERMANN, Stefan VOLKWEIN, 2017. POD-based error control for reduced-order bicriterial PDE-constrained optimization. In: Annual Reviews in Control. 2017, 44, pp. 226-237. ISSN 1367-5788. eISSN 1872-9088. Available under: doi: 10.1016/j.arcontrol.2017.09.004
BibTex
@article{Banholzer2017PODba-37360.2,
  year={2017},
  doi={10.1016/j.arcontrol.2017.09.004},
  title={POD-based error control for reduced-order bicriterial PDE-constrained optimization},
  volume={44},
  issn={1367-5788},
  journal={Annual Reviews in Control},
  pages={226--237},
  author={Banholzer, Stefan and Beermann, Dennis and Volkwein, Stefan}
}
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