POD-based multiobjective optimal control of PDEs with non-smooth objectives

D. Beermann, M. Dellnitz, S. Peitz, S. Volkwein, in: PAMM, 2018, pp. 51–54.

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Conference Paper | Published | English
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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.
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PAMM
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51-54
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Beermann D, Dellnitz M, Peitz S, Volkwein S. POD-based multiobjective optimal control of PDEs with non-smooth objectives. In: PAMM. ; 2018:51-54. doi:10.1002/pamm.201710015
Beermann, D., Dellnitz, M., Peitz, S., & Volkwein, S. (2018). POD-based multiobjective optimal control of PDEs with non-smooth objectives. In PAMM (pp. 51–54). https://doi.org/10.1002/pamm.201710015
@inproceedings{Beermann_Dellnitz_Peitz_Volkwein_2018, title={POD-based multiobjective optimal control of PDEs with non-smooth objectives}, DOI={10.1002/pamm.201710015}, booktitle={PAMM}, author={Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}, year={2018}, pages={51–54} }
Beermann, Dennis, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein. “POD-Based Multiobjective Optimal Control of PDEs with Non-Smooth Objectives.” In PAMM, 51–54, 2018. https://doi.org/10.1002/pamm.201710015.
D. Beermann, M. Dellnitz, S. Peitz, and S. Volkwein, “POD-based multiobjective optimal control of PDEs with non-smooth objectives,” in PAMM, 2018, pp. 51–54.
Beermann, Dennis, et al. “POD-Based Multiobjective Optimal Control of PDEs with Non-Smooth Objectives.” PAMM, 2018, pp. 51–54, doi:10.1002/pamm.201710015.

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