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Using gradient directions to get global convergence of Newton-type methods

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  • di Serafino, Daniela
  • Toraldo, Gerardo
  • Viola, Marco

Abstract

The renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [2] has driven us to consider a globalization strategy based on SD, which is applicable to any line-search method. In particular, we combine Newton-type directions with scaled SD steps to have suitable descent directions. Scaling the SD directions with a suitable step length makes a significant difference with respect to similar globalization approaches, in terms of both theoretical features and computational behavior. We apply our strategy to Newton’s method and the BFGS method, with computational results that appear interesting compared with the results of well-established globalization strategies devised ad hoc for those methods.

Suggested Citation

  • di Serafino, Daniela & Toraldo, Gerardo & Viola, Marco, 2021. "Using gradient directions to get global convergence of Newton-type methods," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300320305671
    DOI: 10.1016/j.amc.2020.125612
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    References listed on IDEAS

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    1. di Serafino, Daniela & Ruggiero, Valeria & Toraldo, Gerardo & Zanni, Luca, 2018. "On the steplength selection in gradient methods for unconstrained optimization," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 176-195.
    2. Crisci, Serena & Ruggiero, Valeria & Zanni, Luca, 2019. "Steplength selection in gradient projection methods for box-constrained quadratic programs," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 312-327.
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    Cited by:

    1. Silvia Berra & Alessandro Torraca & Federico Benvenuto & Sara Sommariva, 2024. "Combined Newton-Gradient Method for Constrained Root-Finding in Chemical Reaction Networks," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 404-427, January.

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