@article{Banholzer2021ROMba-52995.2,
  year={2021},
  doi={10.3390/mca26020032},
  title={ROM-based inexact subdivision methods for PDE-constrained multiobjective optimization},
  number={2},
  volume={26},
  issn={2297-8747},
  journal={Mathematical and Computational Applications},
  author={Banholzer, Stefan and Gebken, Bennet and Reichle, Lena and Volkwein, Stefan},
  note={Article Number: 32}
}

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    <dc:contributor>Volkwein, Stefan</dc:contributor>
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    <dc:contributor>Reichle, Lena</dc:contributor>
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    <dc:contributor>Banholzer, Stefan</dc:contributor>
    <dc:contributor>Gebken, Bennet</dc:contributor>
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    <dcterms:abstract xml:lang="eng">The goal in multiobjective optimization is to determine the so-called Pareto set. Our optimization problem is governed by a parameter dependent semilinear elliptic partial differential equation (PDE). To solve it, we use a gradient based set-oriented numerical method. The numerical solution of the PDE by standard discretization methods usually leads to high computational effort. To overcome this difficulty, reduced-order modeling (ROM) is developed utilizing the reduced basis method. These model simplifications cause inexactness in the gradients. For that reason, an additional descent condition is proposed. Applying a modified subdivision algorithm, numerical experiments illustrate the efficiency of our solution approach.</dcterms:abstract>
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    <dc:creator>Volkwein, Stefan</dc:creator>
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