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On the convergence and mesh-independent property of the Barzilai–Borwein method for PDE-constrained optimization

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2022

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Kunisch, Karl

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https://doi.org/10.1093/imanum/drab056
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IMA Journal of Numerical Analysis. Oxford University Press (OUP). 2022, 42(4), pp. 2984-3021. ISSN 0272-4979. eISSN 1464-3642. Available under: doi: 10.1093/imanum/drab056

Zusammenfassung

Aiming at optimization problems governed by partial differential equations (PDEs), local R-linear convergence of the Barzilai–Borwein (BB) method for a class of twice continuously Fréchet-differentiable functions is proven. Relying on this result, the mesh-independent principle for the BB-method is investigated. The applicability of the theoretical results is demonstrated for two different types of PDE-constrained optimization problems. Numerical experiments are given, which illustrate the theoretical results.

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ISO 690AZMI, Behzad, Karl KUNISCH, 2022. On the convergence and mesh-independent property of the Barzilai–Borwein method for PDE-constrained optimization. In: IMA Journal of Numerical Analysis. Oxford University Press (OUP). 2022, 42(4), pp. 2984-3021. ISSN 0272-4979. eISSN 1464-3642. Available under: doi: 10.1093/imanum/drab056
BibTex
@article{Azmi2022conve-56315,
  year={2022},
  doi={10.1093/imanum/drab056},
  title={On the convergence and mesh-independent property of the Barzilai–Borwein method for PDE-constrained optimization},
  number={4},
  volume={42},
  issn={0272-4979},
  journal={IMA Journal of Numerical Analysis},
  pages={2984--3021},
  author={Azmi, Behzad and Kunisch, Karl}
}
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