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Scaling on the Spectral Gradient Method

Author

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  • Fahimeh Biglari

    (Urmia University of Technology)

  • Maghsud Solimanpur

    (Urmia University)

Abstract

This paper presents a new method for steplength selection in the frame of spectral gradient methods. The steplength formula is based on the interpolation scheme as well as some modified secant equations. The corresponding algorithm selects the initial positive steplength per iteration according to the satisfaction of the secant condition, and then a backtracking procedure along the negative gradient is performed. The numerical experience shows that this algorithm improves favorably the efficiency property of the standard Barzilai–Borwein method as well as some other recently modified Barzilai–Borwein approaches.

Suggested Citation

  • Fahimeh Biglari & Maghsud Solimanpur, 2013. "Scaling on the Spectral Gradient Method," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 626-635, August.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:2:d:10.1007_s10957-012-0265-5
    DOI: 10.1007/s10957-012-0265-5
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    References listed on IDEAS

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    1. J. Z. Zhang & N. Y. Deng & L. H. Chen, 1999. "New Quasi-Newton Equation and Related Methods for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 147-167, July.
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    Cited by:

    1. Hongwei Liu & Zexian Liu, 2019. "An Efficient Barzilai–Borwein Conjugate Gradient Method for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 879-906, March.
    2. Hassan Mohammad & Mohammed Yusuf Waziri, 2019. "Structured Two-Point Stepsize Gradient Methods for Nonlinear Least Squares," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 298-317, April.
    3. Zexian Liu & Hongwei Liu, 2019. "An Efficient Gradient Method with Approximately Optimal Stepsize Based on Tensor Model for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 608-633, May.

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