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Analysis of the Barzilai-Borwein Step-Sizes for Problems in Hilbert Spaces

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2020

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Kunisch, Karl

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https://doi.org/10.1007/s10957-020-01677-y
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Open Access-Veröffentlichung

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Published

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Journal of Optimization Theory and Applications. Springer. 2020, 185(3), pp. 819-844. ISSN 0022-3239. eISSN 1573-2878. Available under: doi: 10.1007/s10957-020-01677-y

Zusammenfassung

The Barzilai and Borwein gradient method has received a significant amount of attention in different fields of optimization. This is due to its simplicity, computational cheapness, and efficiency in practice. In this research, based on spectral analysis techniques, root-linear global convergence for the Barzilai and Borwein method is proven for strictly convex quadratic problems posed in infinite-dimensional Hilbert spaces. The applicability of these results is demonstrated for two optimization problems governed by partial differential equations.

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Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Barzilai–Borwein method, Hilbert spaces, R-Linear rate of convergence, PDE-constrained optimization

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ISO 690AZMI, Behzad, Karl KUNISCH, 2020. Analysis of the Barzilai-Borwein Step-Sizes for Problems in Hilbert Spaces. In: Journal of Optimization Theory and Applications. Springer. 2020, 185(3), pp. 819-844. ISSN 0022-3239. eISSN 1573-2878. Available under: doi: 10.1007/s10957-020-01677-y
BibTex
@article{Azmi2020Analy-56297,
  year={2020},
  doi={10.1007/s10957-020-01677-y},
  title={Analysis of the Barzilai-Borwein Step-Sizes for Problems in Hilbert Spaces},
  number={3},
  volume={185},
  issn={0022-3239},
  journal={Journal of Optimization Theory and Applications},
  pages={819--844},
  author={Azmi, Behzad and Kunisch, Karl}
}
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