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

• Published in: Proceedings in applied mathematics and mechanics Vol. 17; no. 1; pp. 51 - 54
• Main Authors: Beermann, Dennis, Dellnitz, Michael, Peitz, Sebastian, Volkwein, Stefan
• Format: Journal Article
• Language: English
• Published: Berlin WILEY‐VCH Verlag 01-12-2017
• ISSN: 1617-7061; 1617-7061
• DOI: 10.1002/pamm.201710015

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)