POD‐based multiobjective optimal control of PDEs with non‐smooth objectives
A framework for set‐oriented multiobjective optimal control of partial differential equations using reduced order modeling has recently been developed [1]. Following concepts from localized reduced bases methods, error estimators for the reduced cost functionals are utilized to construct a library o...
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| Published in: | Proceedings in applied mathematics and mechanics Vol. 17; no. 1; pp. 51 - 54 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Berlin
WILEY‐VCH Verlag
01-12-2017
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| Abstract | A framework for set‐oriented multiobjective optimal control of partial differential equations using reduced order modeling has recently been developed [1]. 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. Using an academic example, we show that the extension to non‐smooth problems can be realized in a straightforward manner. We then discuss the implications on the numerical results. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| AbstractList | A framework for set‐oriented multiobjective optimal control of partial differential equations using reduced order modeling has recently been developed [1]. 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. Using an academic example, we show that the extension to non‐smooth problems can be realized in a straightforward manner. We then discuss the implications on the numerical results. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
| Author | Dellnitz, Michael Peitz, Sebastian Volkwein, Stefan Beermann, Dennis |
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| Cites_doi | 10.1007/978-3-319-64063-1_7 10.1007/978-3-319-39929-4_37 10.1017/CBO9780511919701 |
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| Copyright | Copyright © 2017 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim |
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| Title | POD‐based multiobjective optimal control of PDEs with non‐smooth objectives |
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