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

Beermann Dennis | Zendy; Dellnitz Michael | Zendy; Peitz Sebastian | Zendy; Volkwein Stefan | Zendy

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

Author(s) -

Beermann Dennis,

Dellnitz Michael,

Peitz Sebastian,

Volkwein Stefan

Publication year - 2017

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.201710015

Subject(s) - extension (predicate logic) , estimator , mathematical optimization , set (abstract data type) , pareto principle , partial differential equation , computer science , construct (python library) , mathematics , order (exchange) , pareto optimal , optimal control , control (management) , multi objective optimization , statistics , artificial intelligence , mathematical analysis , programming language , finance , economics

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)

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