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Descent Symmetrization of the Dai–Liao Conjugate Gradient Method

Author

Listed:
  • Saman Babaie-Kafaki

    (Faculty of Mathematics, Statistics and Computer Science, Semnan University, P. O. Box 35195-363, Semnan, Iran)

  • Reza Ghanbari

    (Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 9177948953, Mashhad, Iran)

Abstract

Symmetrizing the Dai–Liao (DL) search direction matrix by a rank-one modification, we propose a one-parameter class of nonlinear conjugate gradient (CG) methods which includes the memoryless Broyden–Fletcher–Goldfarb–Shanno (MLBFGS) quasi-Newton updating formula. Then, conducting an eigenvalue analysis, we suggest two choices for the parameter of the proposed class of CG methods which simultaneously guarantee the descent property and well-conditioning of the search direction matrix. A global convergence analysis is made for uniformly convex objective functions. Computational experiments are done on a set of unconstrained optimization test problems of the CUTEr collection. Results of numerical comparisons made by the Dolan–Moré performance profile show that proper choices for the mentioned parameter may lead to promising computational performances.

Suggested Citation

  • Saman Babaie-Kafaki & Reza Ghanbari, 2016. "Descent Symmetrization of the Dai–Liao Conjugate Gradient Method," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(02), pages 1-10, April.
    • Handle: RePEc:wsi:apjorx:v:33:y:2016:i:02:n:s0217595916500081
    DOI: 10.1142/S0217595916500081
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    References listed on IDEAS

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    1. Avinoam Perry, 1976. "A Modified Conjugate Gradient Algorithm," Discussion Papers 229, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Kaori Sugiki & Yasushi Narushima & Hiroshi Yabe, 2012. "Globally Convergent Three-Term Conjugate Gradient Methods that Use Secant Conditions and Generate Descent Search Directions for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 733-757, June.
    3. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, June.
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