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

Author

Listed:
  • Predrag S. Stanimirović

    (University of Niš)

  • Branislav Ivanov

    (University of Belgrade)

  • Snežana Djordjević

    (University of Niš)

  • Ivona Brajević

    (University of Niš)

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.

Suggested Citation

  • Predrag S. Stanimirović & Branislav Ivanov & Snežana Djordjević & Ivona Brajević, 2018. "New Hybrid Conjugate Gradient and Broyden–Fletcher–Goldfarb–Shanno Conjugate Gradient Methods," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 860-884, September.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:3:d:10.1007_s10957-018-1324-3
    DOI: 10.1007/s10957-018-1324-3
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    References listed on IDEAS

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    1. Y.H. Dai & Y. Yuan, 2001. "An Efficient Hybrid Conjugate Gradient Method for Unconstrained Optimization," Annals of Operations Research, Springer, vol. 103(1), pages 33-47, March.
    2. Bakhtawar Baluch & Zabidin Salleh & Ahmad Alhawarat & U. A. M. Roslan, 2017. "A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence," Journal of Mathematics, Hindawi, vol. 2017, pages 1-12, September.
    3. Yutao Zheng & Bing Zheng, 2017. "Two New Dai–Liao-Type Conjugate Gradient Methods for Unconstrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 502-509, November.
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    Cited by:

    1. Xiaoyu Wu & Hu Shao & Pengjie Liu & Yue Zhuo, 2023. "An Inertial Spectral CG Projection Method Based on the Memoryless BFGS Update," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1130-1155, September.

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