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Compact representations of structured BFGS matrices

Author

Listed:
  • Johannes J. Brust

    (Argonne National Laboratory)

  • Zichao (Wendy) Di

    (Argonne National Laboratory)

  • Sven Leyffer

    (Argonne National Laboratory)

  • Cosmin G. Petra

    (Lawrence Livermore National Laboratory)

Abstract

For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional structure, recent structured quasi-Newton methods exploit available second-derivative information and approximate unavailable second derivatives. This article develops the compact representations of two structured Broyden-Fletcher-Goldfarb-Shanno update formulas. The compact representations enable efficient limited memory and initialization strategies. Two limited memory line search algorithms are described for which extensive numerical results demonstrate the efficacy of the algorithms, including comparisons to IPOPT on large machine learning problems, and to L-BFGS on a real world large scale ptychographic imaging application.

Suggested Citation

  • Johannes J. Brust & Zichao (Wendy) Di & Sven Leyffer & Cosmin G. Petra, 2021. "Compact representations of structured BFGS matrices," Computational Optimization and Applications, Springer, vol. 80(1), pages 55-88, September.
    • Handle: RePEc:spr:coopap:v:80:y:2021:i:1:d:10.1007_s10589-021-00297-0
    DOI: 10.1007/s10589-021-00297-0
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    References listed on IDEAS

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    1. Johannes Brust & Oleg Burdakov & Jennifer B. Erway & Roummel F. Marcia, 2019. "A dense initialization for limited-memory quasi-Newton methods," Computational Optimization and Applications, Springer, vol. 74(1), pages 121-142, September.
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    Cited by:

    1. Espinoza, Oscar & Corradi, Bruno & González, Luis & Sandoval, Luis & McGinn, Noel & Maldonado, Karina & Larrondo, Yahira, 2023. "The effects of free tuition on the persistence of university students in Chile," International Journal of Educational Development, Elsevier, vol. 101(C).

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