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A delayed weighted gradient method for strictly convex quadratic minimization

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  • Harry Fernando Oviedo Leon

    (CIMAT A.C.)

Abstract

In this paper is developed an accelerated version of the steepest descent method by a two-step iteration. The new algorithm uses information with delay to define the iterations. Specifically, in the first step, a prediction of the new test point is calculated by using the gradient method with the exact minimal gradient steplength and then, a correction is computed by a weighted sum between the prediction and the predecessor iterate of the current point. A convergence result is provided. In order to compare the efficiency and effectiveness of the proposal, with similar methods existing in the literature, numerical experiments are performed. The numerical comparison of the new algorithm with the classical conjugate gradient method shows that our method is a good alternative to solve large-scale problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:74:y:2019:i:3:d:10.1007_s10589-019-00125-6
    DOI: 10.1007/s10589-019-00125-6
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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. 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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    Cited by:

    1. Hugo Lara & Rafael Aleixo & Harry Oviedo, 2024. "Delayed Weighted Gradient Method with simultaneous step-sizes for strongly convex optimization," Computational Optimization and Applications, Springer, vol. 89(1), pages 151-182, September.
    2. Roberto Andreani & Marcos Raydan, 2021. "Properties of the delayed weighted gradient method," Computational Optimization and Applications, Springer, vol. 78(1), pages 167-180, January.

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