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A family of spectral gradient methods for optimization

Author

Listed:
  • Yu-Hong Dai

    (Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

  • Yakui Huang

    (Hebei University of Technology)

  • Xin-Wei Liu

    (Hebei University of Technology)

Abstract

We propose a family of spectral gradient methods, whose stepsize is determined by a convex combination of the long Barzilai–Borwein (BB) stepsize and the short BB stepsize. Each member of the family is shown to share certain quasi-Newton property in the sense of least squares. The family also includes some other gradient methods as its special cases. We prove that the family of methods is R-superlinearly convergent for two-dimensional strictly convex quadratics. Moreover, the family is R-linearly convergent in the any-dimensional case. Numerical results of the family with different settings are presented, which demonstrate that the proposed family is promising.

Suggested Citation

  • Yu-Hong Dai & Yakui Huang & Xin-Wei Liu, 2019. "A family of spectral gradient methods for optimization," Computational Optimization and Applications, Springer, vol. 74(1), pages 43-65, September.
    • Handle: RePEc:spr:coopap:v:74:y:2019:i:1:d:10.1007_s10589-019-00107-8
    DOI: 10.1007/s10589-019-00107-8
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    References listed on IDEAS

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    1. Birgin, Ernesto G. & Martínez, Jose Mario & Raydan, Marcos, 2014. "Spectral Projected Gradient Methods: Review and Perspectives," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i03).
    2. Roberta De Asmundis & Daniela di Serafino & William Hager & Gerardo Toraldo & Hongchao Zhang, 2014. "An efficient gradient method using the Yuan steplength," Computational Optimization and Applications, Springer, vol. 59(3), pages 541-563, December.
    3. Yakui Huang & Hongwei Liu, 2016. "Smoothing projected Barzilai–Borwein method for constrained non-Lipschitz optimization," Computational Optimization and Applications, Springer, vol. 65(3), pages 671-698, December.
    4. 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.
    5. Clóvis Gonzaga & Ruana Schneider, 2016. "On the steepest descent algorithm for quadratic functions," Computational Optimization and Applications, Springer, vol. 63(2), pages 523-542, March.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Yakui Huang & Yu-Hong Dai & Xin-Wei Liu & Hongchao Zhang, 2022. "On the acceleration of the Barzilai–Borwein method," Computational Optimization and Applications, Springer, vol. 81(3), pages 717-740, April.
    2. Masoud Fatemi, 2022. "On initial point selection of the steepest descent algorithm for general quadratic functions," Computational Optimization and Applications, Springer, vol. 82(2), pages 329-360, June.
    3. Roberto Andreani & Marcos Raydan, 2021. "Properties of the delayed weighted gradient method," Computational Optimization and Applications, Springer, vol. 78(1), pages 167-180, January.
    4. Giulia Ferrandi & Michiel E. Hochstenbach & Nataša Krejić, 2023. "A harmonic framework for stepsize selection in gradient methods," Computational Optimization and Applications, Springer, vol. 85(1), pages 75-106, May.
    5. Na Huang, 2022. "On R-linear convergence analysis for a class of gradient methods," Computational Optimization and Applications, Springer, vol. 81(1), pages 161-177, January.

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