POD‐based multiobjective optimal control of PDEs with non‐smooth objectives. Issue 1 (15th March 2018)

• Record Type: Journal Article
• Authors: Beermann, Dennis; Dellnitz, Michael; Peitz, Sebastian; Volkwein, Stefan
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 17:Issue 1(2017)
• Page Start: 51
• Page End: 54
• Publication Date: 2018-03-15
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201710015
• Languages: English
• ISSNs: 1617-7061

Abstract

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)