Publikation: ROM-based inexact subdivision methods for PDE-constrained multiobjective optimization
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2021
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Mathematical and Computational Applications. MDPI. 2021, 26(2), 32. ISSN 2297-8747. eISSN 1300-686X. Available under: doi: 10.3390/mca26020032
Zusammenfassung
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.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
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multiobjective optimization; PDE-constrained optimization; reduced-order modeling; set-oriented methods; inexact optimization
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BANHOLZER, Stefan, Bennet GEBKEN, Lena REICHLE, Stefan VOLKWEIN, 2021. ROM-based inexact subdivision methods for PDE-constrained multiobjective optimization. In: Mathematical and Computational Applications. MDPI. 2021, 26(2), 32. ISSN 2297-8747. eISSN 1300-686X. Available under: doi: 10.3390/mca26020032BibTex
@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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