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Secant Update generalized version of PSB: a new approach

Author

Listed:
  • Nicolas Boutet

    (Royal Military Academy
    Ghent University)

  • Rob Haelterman

    (Royal Military Academy)

  • Joris Degroote

    (Ghent University)

Abstract

In optimization, one of the main challenges of the widely used family of Quasi-Newton methods is to find an estimate of the Hessian matrix as close as possible to the real matrix. In this paper, we develop a new update formula for the estimate of the Hessian starting from the Powell-Symetric-Broyden (PSB) formula and adding pieces of information from the previous steps of the optimization path. This lead to a multisecant version of PSB, which we call generalised PSB (gPSB), but which does not exist in general as was proven before. We provide a novel interpretation of this non-existence. In addition, we provide a formula that satisfies the multisecant condition and is as close to symmetric as possible and vice versa for a second formula. Subsequently, we add enforcement of the last secant equation and present a comparison between the different methods.

Suggested Citation

  • Nicolas Boutet & Rob Haelterman & Joris Degroote, 2021. "Secant Update generalized version of PSB: a new approach," Computational Optimization and Applications, Springer, vol. 78(3), pages 953-982, April.
    • Handle: RePEc:spr:coopap:v:78:y:2021:i:3:d:10.1007_s10589-020-00256-1
    DOI: 10.1007/s10589-020-00256-1
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    References listed on IDEAS

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    1. Nicholas Gould & Dominique Orban & Philippe Toint, 2015. "CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization," Computational Optimization and Applications, Springer, vol. 60(3), pages 545-557, April.
    2. Nicolas Boutet & Rob Haelterman & Joris Degroote, 2020. "Secant update version of quasi-Newton PSB with weighted multisecant equations," Computational Optimization and Applications, Springer, vol. 75(2), pages 441-466, March.
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    Cited by:

    1. E. G. Birgin & J. M. Martínez, 2022. "Accelerated derivative-free nonlinear least-squares applied to the estimation of Manning coefficients," Computational Optimization and Applications, Springer, vol. 81(3), pages 689-715, April.

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