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A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence

Author

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  • Bakhtawar Baluch
  • Zabidin Salleh
  • Ahmad Alhawarat
  • U. A. M. Roslan

Abstract

A new modified three-term conjugate gradient (CG) method is shown for solving the large scale optimization problems. The idea relates to the famous Polak-Ribière-Polyak (PRP) formula. As the numerator of PRP plays a vital role in numerical result and not having the jamming issue, PRP method is not globally convergent. So, for the new three-term CG method, the idea is to use the PRP numerator and combine it with any good CG formula’s denominator that performs well. The new modification of three-term CG method possesses the sufficient descent condition independent of any line search. The novelty is that by using the Wolfe Powell line search the new modification possesses global convergence properties with convex and nonconvex functions. Numerical computation with the Wolfe Powell line search by using the standard test function of optimization shows the efficiency and robustness of the new modification.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jjmath:2715854
    DOI: 10.1155/2017/2715854
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    References listed on IDEAS

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    1. 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.
    2. Mehiddin Al-Baali & Yasushi Narushima & Hiroshi Yabe, 2015. "A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 60(1), pages 89-110, January.
    3. Ahmad Alhawarat & Zabidin Salleh, 2017. "Modification of Nonlinear Conjugate Gradient Method with Weak Wolfe-Powell Line Search," Abstract and Applied Analysis, Hindawi, vol. 2017, pages 1-6, March.
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    1. 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.

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