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A Trust Region Reduced Basis Pascoletti-Serafini Algorithm for Multi-Objective PDE-Constrained Parameter Optimization

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2022

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Mathematical and Computational Applications. MDPI AG. 2022, 27(3), 39. ISSN 1300-686X. eISSN 2297-8747. Available under: doi: 10.3390/mca27030039

Zusammenfassung

In the present paper non-convex multi-objective parameter optimization problems are considered which are governed by elliptic parametrized partial differential equations (PDEs). To solve these problems numerically the Pascoletti-Serafini scalarization is applied and the obtained scalar optimization problems are solved by an augmented Lagrangian method. However, due to the PDE constraints, the numerical solution is very expensive so that a model reduction is utilized by using the reduced basis (RB) method. The quality of the RB approximation is ensured by a trust-region strategy which does not require any offline procedure, in which the RB functions are computed in a greedy algorithm. Moreover, convergence of the proposed method is guaranteed and different techniques to prevent the excessive growth of the number of basis functions are explored. Numerical examples illustrate the efficiency of the proposed solution technique.

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510 Mathematik

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non-convex multi-objective optimization; partial differential equations; Pascoletti-Serafini method; augmented Lagrangian; reduced basis method; trust-region strategy

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ISO 690BANHOLZER, Stefan, Luca MECHELLI, Stefan VOLKWEIN, 2022. A Trust Region Reduced Basis Pascoletti-Serafini Algorithm for Multi-Objective PDE-Constrained Parameter Optimization. In: Mathematical and Computational Applications. MDPI AG. 2022, 27(3), 39. ISSN 1300-686X. eISSN 2297-8747. Available under: doi: 10.3390/mca27030039
BibTex
@article{Banholzer2022-06Trust-57762,
  year={2022},
  doi={10.3390/mca27030039},
  title={A Trust Region Reduced Basis Pascoletti-Serafini Algorithm for Multi-Objective PDE-Constrained Parameter Optimization},
  number={3},
  volume={27},
  issn={1300-686X},
  journal={Mathematical and Computational Applications},
  author={Banholzer, Stefan and Mechelli, Luca and Volkwein, Stefan},
  note={Article Number: 39}
}
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