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A note on hybridization process applied on transformed double step size model

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Abstract

We introduce a hybrid gradient model for solving unconstrained optimization problems based on one specific accelerated gradient iteration. Having applied a three term hybridization relation on transformed accelerated double step size model, we develop an efficient hybrid accelerated scheme. We determine an iterative step size variable using Backtracking line search technique in which we take an optimally calculated starting value for the posed method. In convergence analysis, we show that the proposed method is at least linearly convergent on the sets of uniformly convex functions and strictly convex quadratic functions. Numerical computations confirm a significant improvement compared with some relevant hybrid and accelerated gradient processes. More precisely, subject to the number of iterations, the CPU time metric and the number of evaluations of the objective function, defined process outperforms comparative schemes multiple times.

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Funding

The authors gratefully acknowledge supports from the Ministry of Science of Republic of Serbia, Grant No. 174025 and Grant No. 174024.

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Authors and Affiliations

  1. Faculty of Sciences and Mathematics, University of Priština, Lole Ribara 29, Kosovska Mitrovica, 38220, Serbia

    Milena J. Petrović & Dragana Valjarević

  2. Serbian Academy of Sciences and Arts, Kneza Mihaila 35, Belgrade, 11000, Serbia

    Vladimir Rakočević

  3. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, Niš, 18000, Serbia

    Vladimir Rakočević & Dejan Ilić

Authors
  1. Milena J. Petrović
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  2. Vladimir Rakočević
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  3. Dragana Valjarević
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  4. Dejan Ilić
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Corresponding author

Correspondence to Milena J. Petrović.

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Petrović, M.J., Rakočević, V., Valjarević, D. et al. A note on hybridization process applied on transformed double step size model. Numer Algor 85, 449–465 (2020). https://doi.org/10.1007/s11075-019-00821-8

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  • DOI: https://doi.org/10.1007/s11075-019-00821-8

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