Adaptive reduced basis methods for PDE-constrained optimization and optimal input design

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2022
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In this paper we propose an algorithm for the bi-level optimal input design involving a parameter-dependent evolution problem. In the inner cycle a control is fixed and the parameter is optimized in order to minimize a cost function that measure the discrepancy from some data. In the outer cycle the found parameter is fixed and the control is now optimized in order to minimize a suitable measure of uncertainty of the parameters. The inner cycle uses a trust-region reduced basis approximation of the model with creation and enrichment of the reduced basis on-the-fly. Numerical examples illustrate the efficiency of the proposed approach.In the inner cycle a control is fixed and the parameter is optimized in order to minimize a cost function that measure the discrepancy from some data. In the outer cycle the found parameter is fixed and the control is now optimized in order to minimize a suitable measure of uncertainty of the parameters. The inner cycle uses a trust-region reduced basis approximation of the model with creation and enrichment of the reduced basis on-the-fly. Numerical examples illustrate the efficiency of the proposed approach.

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510 Mathematik
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Reduced basis methods, a-posteriori error, trust-region optimization, evolution problems, optimal input design
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ISO 690PETROCCHI, Andrea, Matthias K. SCHARRER, Stefan VOLKWEIN, 2022. Adaptive reduced basis methods for PDE-constrained optimization and optimal input design
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@techreport{Petrocchi2022Adapt-56711.3,
  year={2022},
  title={Adaptive reduced basis methods for PDE-constrained optimization and optimal input design},
  author={Petrocchi, Andrea and Scharrer, Matthias K. and Volkwein, Stefan},
  note={Corrected and updated version of: <br /> http://nbn-resolving.de/urn:nbn:de:bsz:352-2-1l9b7uuht7b1s0}
}
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Corrected and updated version of:
http://nbn-resolving.de/urn:nbn:de:bsz:352-2-1l9b7uuht7b1s0
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