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

Abstract

A framework for set-oriented multiobjective optimal control of partial differential equations using reduced order modeling has recently been developed \cite{BDPV17}. 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. It is shown that the extension to non-smooth problems can be realized in a straightforward manner and the implications on the numerical results are discussed.