Set-Oriented Multiobjective Optimal Control of PDEs using Proper Orthogonal Decomposition
| Type of Publication: | Contribution to a conference collection |
| Publication status: | Published |
| Author: | Beermann, Dennis; Dellnitz, Michael; Peitz, Sebastian; Volkwein, Stefan |
| Year of publication: | 2018 |
| Conference: | Reduced-Order Modeling for Simulation and Optimization : Powerful Algorithms as Key Enablers for Scientific Computing ; KoMSO Challenge Workshop, Nov 17, 2016 - Nov 18, 2016, Renningen, Germany |
| Published in: | Reduced-Order Modeling (ROM) for Simulation and Optimization : Powerful Algorithms as Key Enablers for Scientific Computing / Keiper, Winfried; Milde, Anja; Volkwein, Stefan (ed.). - Cham : Springer, 2018. - pp. 47-72. - ISBN 978-3-319-75318-8 |
| DOI (citable link): | https://dx.doi.org/10.1007/978-3-319-75319-5_3 |
| Summary: |
In this chapter, we combine a global, derivative-free subdivision algorithm for multiobjective optimization problems with a-posteriori error estimates for reduced-order models based on Proper Orthogonal Decomposition in order to efficiently solve multiobjective optimization problems governed by partial differential equations. An error bound for a semilinear heat equation is developed by which the errors in the conflicting objectives can be estimated individually. The resulting algorithm constructs a library of locally valid reduced-order models online using a Greedy (worst-first) search. Using this approach, the number of evaluations of the full-order model can be reduced by a factor of more than 1000.
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| Subject (DDC): | 510 Mathematics |
| Keywords: | Multiobjective optimization, PDE-constrained optimization, reduced-order modeling, set-oriented methods |
| Bibliography of Konstanz: | Yes |
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BEERMANN, Dennis, Michael DELLNITZ, Sebastian PEITZ, Stefan VOLKWEIN, 2018. Set-Oriented Multiobjective Optimal Control of PDEs using Proper Orthogonal Decomposition. Reduced-Order Modeling for Simulation and Optimization : Powerful Algorithms as Key Enablers for Scientific Computing ; KoMSO Challenge Workshop. Renningen, Germany, Nov 17, 2016 - Nov 18, 2016. In: KEIPER, Winfried, ed., Anja MILDE, ed., Stefan VOLKWEIN, ed.. Reduced-Order Modeling (ROM) for Simulation and Optimization : Powerful Algorithms as Key Enablers for Scientific Computing. Cham:Springer, pp. 47-72. ISBN 978-3-319-75318-8. Available under: doi: 10.1007/978-3-319-75319-5_3
@inproceedings{Beermann2018SetOr-38752, title={Set-Oriented Multiobjective Optimal Control of PDEs using Proper Orthogonal Decomposition}, year={2018}, doi={10.1007/978-3-319-75319-5_3}, isbn={978-3-319-75318-8}, address={Cham}, publisher={Springer}, booktitle={Reduced-Order Modeling (ROM) for Simulation and Optimization : Powerful Algorithms as Key Enablers for Scientific Computing}, pages={47--72}, editor={Keiper, Winfried and Milde, Anja and Volkwein, Stefan}, author={Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan} }
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