{"publication":"Reduced-Order Modeling (ROM) for Simulation and Optimization","date_updated":"2022-01-06T07:04:00Z","type":"book_chapter","page":"47-72","doi":"10.1007/978-3-319-75319-5_3","publication_status":"published","language":[{"iso":"eng"}],"date_created":"2019-03-29T13:31:20Z","citation":{"mla":"Beermann, Dennis, et al. “Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition.” <i>Reduced-Order Modeling (ROM) for Simulation and Optimization</i>, 2018, pp. 47–72, doi:<a href=\"https://doi.org/10.1007/978-3-319-75319-5_3\">10.1007/978-3-319-75319-5_3</a>.","ama":"Beermann D, Dellnitz M, Peitz S, Volkwein S. Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition. In: <i>Reduced-Order Modeling (ROM) for Simulation and Optimization</i>. Cham; 2018:47-72. doi:<a href=\"https://doi.org/10.1007/978-3-319-75319-5_3\">10.1007/978-3-319-75319-5_3</a>","ieee":"D. Beermann, M. Dellnitz, S. Peitz, and S. Volkwein, “Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition,” in <i>Reduced-Order Modeling (ROM) for Simulation and Optimization</i>, Cham, 2018, pp. 47–72.","apa":"Beermann, D., Dellnitz, M., Peitz, S., &#38; Volkwein, S. (2018). Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition. In <i>Reduced-Order Modeling (ROM) for Simulation and Optimization</i> (pp. 47–72). Cham. <a href=\"https://doi.org/10.1007/978-3-319-75319-5_3\">https://doi.org/10.1007/978-3-319-75319-5_3</a>","bibtex":"@inbook{Beermann_Dellnitz_Peitz_Volkwein_2018, place={Cham}, title={Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-75319-5_3\">10.1007/978-3-319-75319-5_3</a>}, booktitle={Reduced-Order Modeling (ROM) for Simulation and Optimization}, author={Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}, year={2018}, pages={47–72} }","chicago":"Beermann, Dennis, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein. “Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition.” In <i>Reduced-Order Modeling (ROM) for Simulation and Optimization</i>, 47–72. Cham, 2018. <a href=\"https://doi.org/10.1007/978-3-319-75319-5_3\">https://doi.org/10.1007/978-3-319-75319-5_3</a>.","short":"D. Beermann, M. Dellnitz, S. Peitz, S. Volkwein, in: Reduced-Order Modeling (ROM) for Simulation and Optimization, Cham, 2018, pp. 47–72."},"user_id":"47427","department":[{"_id":"101"}],"publication_identifier":{"isbn":["9783319753188","9783319753195"]},"title":"Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition","_id":"8754","abstract":[{"text":"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 in such a way that 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.","lang":"eng"}],"author":[{"last_name":"Beermann","full_name":"Beermann, Dennis","first_name":"Dennis"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"},{"full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X"},{"full_name":"Volkwein, Stefan","last_name":"Volkwein","first_name":"Stefan"}],"place":"Cham","year":"2018","project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"status":"public"}