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Properties of the delayed weighted gradient method

Author

Listed:
  • Roberto Andreani

    (University of Campinas)

  • Marcos Raydan

    (Centro de Matemática e Aplicações (CMA), FCT, UNL)

Abstract

The delayed weighted gradient method, recently introduced in Oviedo-Leon (Comput Optim Appl 74:729–746, 2019), is a low-cost gradient-type method that exhibits a surprisingly and perhaps unexpected fast convergence behavior that competes favorably with the well-known conjugate gradient method for the minimization of convex quadratic functions. In this work, we establish several orthogonality properties that add understanding to the practical behavior of the method, including its finite termination. We show that if the $$n\times n$$ n × n real Hessian matrix of the quadratic function has only $$p

Suggested Citation

  • Roberto Andreani & Marcos Raydan, 2021. "Properties of the delayed weighted gradient method," Computational Optimization and Applications, Springer, vol. 78(1), pages 167-180, January.
    • Handle: RePEc:spr:coopap:v:78:y:2021:i:1:d:10.1007_s10589-020-00232-9
    DOI: 10.1007/s10589-020-00232-9
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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. 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.
    3. 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.
    4. Harry Fernando Oviedo Leon, 2019. "A delayed weighted gradient method for strictly convex quadratic minimization," Computational Optimization and Applications, Springer, vol. 74(3), pages 729-746, December.
    5. 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.
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