Publikation: POD-based multiobjective optimal control of PDEs with non-smooth objectives
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2017
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KÖNKE, Carsten, ed. and others. Special issue: 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM). Weinheim: Wiley, 2017, pp. 51-54. Proceedings in Applied Mathematics and Mechanics (PAMM). 17,1. eISSN 1617-7061. Available under: doi: 10.1002/pamm.201710015
Zusammenfassung
A framework for set-oriented multiobjective optimal control of partial differential equations using reduced order modeling has recently been developed \cite{BDPV17}. Following concepts from localized reduced bases methods, error estimators for the reduced cost functionals are utilized to construct a library of locally valid reduced order models. This way, a superset of the Pareto set can efficiently be computed while maintaining a prescribed error bound. In this article, this algorithm is applied to a problem with non-smooth objective functionals. It is shown that the extension to non-smooth problems can be realized in a straightforward manner and the implications on the numerical results are discussed.
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510 Mathematik
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88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), 6. März 2017 - 10. März 2017, Weimar
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BEERMANN, Dennis, Michael DELLNITZ, Sebastian PEITZ, Stefan VOLKWEIN, 2017. POD-based multiobjective optimal control of PDEs with non-smooth objectives. 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM). Weimar, 6. März 2017 - 10. März 2017. In: KÖNKE, Carsten, ed. and others. Special issue: 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM). Weinheim: Wiley, 2017, pp. 51-54. Proceedings in Applied Mathematics and Mechanics (PAMM). 17,1. eISSN 1617-7061. Available under: doi: 10.1002/pamm.201710015BibTex
@inproceedings{Beermann2017PODba-39338.2,
year={2017},
doi={10.1002/pamm.201710015},
title={POD-based multiobjective optimal control of PDEs with non-smooth objectives},
number={17,1},
publisher={Wiley},
address={Weinheim},
series={Proceedings in Applied Mathematics and Mechanics (PAMM)},
booktitle={Special issue: 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)},
pages={51--54},
editor={Könke, Carsten},
author={Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}
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