@inbook{8754,
  abstract     = {{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.}},
  author       = {{Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}},
  booktitle    = {{Reduced-Order Modeling (ROM) for Simulation and Optimization}},
  isbn         = {{9783319753188}},
  pages        = {{47--72}},
  title        = {{{Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition}}},
  doi          = {{10.1007/978-3-319-75319-5_3}},
  year         = {{2018}},
}