[{"doi":"10.1002/pamm.201710015","user_id":"47427","language":[{"iso":"eng"}],"_id":"8757","page":"51-54","date_updated":"2022-01-06T07:04:00Z","publication_status":"published","publication_identifier":{"issn":["1617-7061"]},"author":[{"last_name":"Beermann","first_name":"Dennis","full_name":"Beermann, Dennis"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"},{"id":"47427","orcid":"https://orcid.org/0000-0002-3389-793X","first_name":"Sebastian","last_name":"Peitz","full_name":"Peitz, Sebastian"},{"full_name":"Volkwein, Stefan","first_name":"Stefan","last_name":"Volkwein"}],"status":"public","title":"POD-based multiobjective optimal control of PDEs with non-smooth objectives","year":"2018","department":[{"_id":"101"}],"type":"conference","date_created":"2019-03-29T13:34:25Z","project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"abstract":[{"lang":"eng","text":"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."}],"citation":{"ieee":"D. Beermann, M. Dellnitz, S. Peitz, and S. Volkwein, “POD-based multiobjective optimal control of PDEs with non-smooth objectives,” in <i>PAMM</i>, 2018, pp. 51–54.","apa":"Beermann, D., Dellnitz, M., Peitz, S., &#38; Volkwein, S. (2018). POD-based multiobjective optimal control of PDEs with non-smooth objectives. In <i>PAMM</i> (pp. 51–54). <a href=\"https://doi.org/10.1002/pamm.201710015\">https://doi.org/10.1002/pamm.201710015</a>","chicago":"Beermann, Dennis, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein. “POD-Based Multiobjective Optimal Control of PDEs with Non-Smooth Objectives.” In <i>PAMM</i>, 51–54, 2018. <a href=\"https://doi.org/10.1002/pamm.201710015\">https://doi.org/10.1002/pamm.201710015</a>.","short":"D. Beermann, M. Dellnitz, S. Peitz, S. Volkwein, in: PAMM, 2018, pp. 51–54.","mla":"Beermann, Dennis, et al. “POD-Based Multiobjective Optimal Control of PDEs with Non-Smooth Objectives.” <i>PAMM</i>, 2018, pp. 51–54, doi:<a href=\"https://doi.org/10.1002/pamm.201710015\">10.1002/pamm.201710015</a>.","bibtex":"@inproceedings{Beermann_Dellnitz_Peitz_Volkwein_2018, title={POD-based multiobjective optimal control of PDEs with non-smooth objectives}, DOI={<a href=\"https://doi.org/10.1002/pamm.201710015\">10.1002/pamm.201710015</a>}, booktitle={PAMM}, author={Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}, year={2018}, pages={51–54} }","ama":"Beermann D, Dellnitz M, Peitz S, Volkwein S. POD-based multiobjective optimal control of PDEs with non-smooth objectives. In: <i>PAMM</i>. ; 2018:51-54. doi:<a href=\"https://doi.org/10.1002/pamm.201710015\">10.1002/pamm.201710015</a>"},"publication":"PAMM"}]