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A class of adaptive Dai–Liao conjugate gradient methods based on the scaled memoryless BFGS update

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  • Saman Babaie-Kafaki

    (Semnan University)

  • Reza Ghanbari

    (Ferdowsi University of Mashhad)

Abstract

Minimizing the distance between search direction matrix of the Dai–Liao method and the scaled memoryless BFGS update in the Frobenius norm, and using Powell’s nonnegative restriction of the conjugate gradient parameters, a one-parameter class of nonlinear conjugate gradient methods is proposed. Then, a brief global convergence analysis is made with and without convexity assumption on the objective function. Preliminary numerical results are reported; they demonstrate a proper choice for the parameter of the proposed class of conjugate gradient methods may lead to promising numerical performance.

Suggested Citation

  • Saman Babaie-Kafaki & Reza Ghanbari, 2017. "A class of adaptive Dai–Liao conjugate gradient methods based on the scaled memoryless BFGS update," 4OR, Springer, vol. 15(1), pages 85-92, March.
    • Handle: RePEc:spr:aqjoor:v:15:y:2017:i:1:d:10.1007_s10288-016-0323-1
    DOI: 10.1007/s10288-016-0323-1
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    References listed on IDEAS

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    1. Shmuel S. Oren, 1974. "Self-Scaling Variable Metric (SSVM) Algorithms," Management Science, INFORMS, vol. 20(5), pages 863-874, January.
    2. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, December.
    3. Babaie-Kafaki, Saman & Ghanbari, Reza, 2014. "The Dai–Liao nonlinear conjugate gradient method with optimal parameter choices," European Journal of Operational Research, Elsevier, vol. 234(3), pages 625-630.
    4. Shmuel S. Oren & David G. Luenberger, 1974. "Self-Scaling Variable Metric (SSVM) Algorithms," Management Science, INFORMS, vol. 20(5), pages 845-862, January.
    5. Andrei, Neculai, 2010. "Accelerated scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization," European Journal of Operational Research, Elsevier, vol. 204(3), pages 410-420, August.
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    Cited by:

    1. Parvaneh Faramarzi & Keyvan Amini, 2021. "A spectral three-term Hestenes–Stiefel conjugate gradient method," 4OR, Springer, vol. 19(1), pages 71-92, March.

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