Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition

  • Dennis Beermann
  • Michael Dellnitz
  • Sebastian Peitz
  • Stefan VolkweinEmail author


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.



This work is supported by the Priority Programme SPP 1962 Non-smooth and Complementarity-based Distributed Parameter Systems of the German Research Foundation (DFG) and by the project Hybrides Planungsverfahren zur energieeffizienten Wärme- und Stromversorgung von städtischen Verteilnetzen funded by the German Ministry for Economic Affairs and Energy.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Dennis Beermann
    • 1
  • Michael Dellnitz
    • 2
  • Sebastian Peitz
    • 2
  • Stefan Volkwein
    • 1
    Email author
  1. 1.Department of Mathematics and StatisticsUniversity of KonstanzKonstanzGermany
  2. 2.Department of MathematicsPaderborn UniversityPaderbornGermany

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