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Multiobjective PDE-constrained optimization using the reduced-basis method

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2017

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Ulbrich, Stefan

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https://doi.org/10.1007/s10444-016-9512-x
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Advances in Computational Mathematics. 2017, 43(5), pp. 945-972. ISSN 1019-7168. eISSN 1572-9044. Available under: doi: 10.1007/s10444-016-9512-x

Zusammenfassung

In this paper the reduced basis (RB) method is applied to solve quadratic multiobjective optimal control problems governed by linear parametrized variational equations. These problems often arise in applications, where the quality of the system behavior has to be measured by more than one criterium. The weighted sum method is exploited for defining scalar-valued linear-quadratic optimal control problems built by introducing additional optimization parameters. The optimal controls corresponding to specific choices of the optimization parameters are efficiently computed by the RB method. The accuracy is guaranteed by an a-posteriori error estimate. An effective sensitivity analysis allows to further reduce the computational times for identifying a suitable and representative set of optimal controls.

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510 Mathematik

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ISO 690IAPICHINO, Laura, Stefan ULBRICH, Stefan VOLKWEIN, 2017. Multiobjective PDE-constrained optimization using the reduced-basis method. In: Advances in Computational Mathematics. 2017, 43(5), pp. 945-972. ISSN 1019-7168. eISSN 1572-9044. Available under: doi: 10.1007/s10444-016-9512-x
BibTex
@article{Iapichino2017-10Multi-40990,
  year={2017},
  doi={10.1007/s10444-016-9512-x},
  title={Multiobjective PDE-constrained optimization using the reduced-basis method},
  number={5},
  volume={43},
  issn={1019-7168},
  journal={Advances in Computational Mathematics},
  pages={945--972},
  author={Iapichino, Laura and Ulbrich, Stefan and Volkwein, Stefan}
}
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