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An Efficient Hybrid Conjugate Gradient Method with the Strong Wolfe-Powell Line Search

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Listed:
  • Ahmad Alhawarat
  • Mustafa Mamat
  • Mohd Rivaie
  • Zabidin Salleh

Abstract

Conjugate gradient (CG) method is an interesting tool to solve optimization problems in many fields, such as design, economics, physics, and engineering. In this paper, we depict a new hybrid of CG method which relates to the famous Polak-Ribière-Polyak (PRP) formula. It reveals a solution for the PRP case which is not globally convergent with the strong Wolfe-Powell (SWP) line search. The new formula possesses the sufficient descent condition and the global convergent properties. In addition, we further explained about the cases where PRP method failed with SWP line search. Furthermore, we provide numerical computations for the new hybrid CG method which is almost better than other related PRP formulas in both the number of iterations and the CPU time under some standard test functions.

Suggested Citation

  • Ahmad Alhawarat & Mustafa Mamat & Mohd Rivaie & Zabidin Salleh, 2015. "An Efficient Hybrid Conjugate Gradient Method with the Strong Wolfe-Powell Line Search," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-7, July.
    • Handle: RePEc:hin:jnlmpe:103517
    DOI: 10.1155/2015/103517
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