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New Hybrid Conjugate Gradient and Broyden–Fletcher–Goldfarb–Shanno Conjugate Gradient Methods

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Abstract

Three hybrid methods for solving unconstrained optimization problems are introduced. These methods are defined using proper combinations of the search directions and included parameters in conjugate gradient and quasi-Newton methods. The convergence of proposed methods with the underlying backtracking line search is analyzed for general objective functions and particularly for uniformly convex objective functions. Numerical experiments show the superiority of the proposed methods with respect to some existing methods in view of the Dolan and Moré’s performance profile.

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Acknowledgements

The first author gratefully acknowledge support from the Research Project 174013 of the Serbian Ministry of Science.

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Authors and Affiliations

  1. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18 000, Nis, Serbia

    Predrag S. Stanimirović & Ivona Brajević

  2. Technical Faculty in Bor, University of Belgrade, Vojske Jugoslavije 12, 19 210, Bor, Serbia

    Branislav Ivanov

  3. Faculty of Technology in Leskovac, University of Niš, Bulevar Oslobodjenja 124, 16 000, Leskovac, Serbia

    Snežana Djordjević

Authors
  1. Predrag S. Stanimirović
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  2. Branislav Ivanov
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  3. Snežana Djordjević
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  4. Ivona Brajević
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Corresponding author

Correspondence to Predrag S. Stanimirović.

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Communicated by Ilio Galligani.

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Stanimirović, P.S., Ivanov, B., Djordjević, S. et al. New Hybrid Conjugate Gradient and Broyden–Fletcher–Goldfarb–Shanno Conjugate Gradient Methods. J Optim Theory Appl 178, 860–884 (2018). https://doi.org/10.1007/s10957-018-1324-3

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  • DOI: https://doi.org/10.1007/s10957-018-1324-3

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