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An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization Problem

Author

Listed:
  • Ahmad Alhawarat
  • Thoi Trung Nguyen
  • Ramadan Sabra
  • Zabidin Salleh
  • Qingli Zhao

Abstract

To find a solution of unconstrained optimization problems, we normally use a conjugate gradient (CG) method since it does not cost memory or storage of second derivative like Newton’s method or Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. Recently, a new modification of Polak and Ribiere method was proposed with new restart condition to give a so-call AZPRP method. In this paper, we propose a new modification of AZPRP CG method to solve large-scale unconstrained optimization problems based on a modification of restart condition. The new parameter satisfies the descent property and the global convergence analysis with the strong Wolfe-Powell line search. The numerical results prove that the new CG method is strongly aggressive compared with CG_Descent method. The comparisons are made under a set of more than 140 standard functions from the CUTEst library. The comparison includes number of iterations and CPU time.

Suggested Citation

  • Ahmad Alhawarat & Thoi Trung Nguyen & Ramadan Sabra & Zabidin Salleh & Qingli Zhao, 2021. "An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization Problem," Journal of Mathematics, Hindawi, vol. 2021, pages 1-9, April.
    • Handle: RePEc:hin:jjmath:6692024
    DOI: 10.1155/2021/6692024
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