An efficient hybrid conjugate gradient method for unconstrained optimization

Abdulkarim Hassan Ibrahim*, Poom Kumam, Ahmad Kamandi, Auwal Bala Abubakar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In this paper, we propose a hybrid conjugate gradient method for unconstrained optimization, obtained by a convex combination of the LS and KMD conjugate gradient parameters. A favourite property of the proposed method is that the search direction satisfies the Dai–Liao conjugacy condition and the quasi-Newton direction. In addition, this property does not depend on the line search. Under a modified strong Wolfe line search, we establish the global convergence of the method. Numerical comparison using a set of 109 unconstrained optimization test problems from the CUTEst library show that the proposed method outperforms the Liu–Storey and Hager–Zhang conjugate gradient methods.

Original languageEnglish
JournalOptimization Methods and Software
Publication statusAccepted/In press - 2022
Externally publishedYes


  • CUTEst
  • Dai–Liao conjugacy
  • Quasi-Newton direction
  • Unconstrained optimization
  • conjugate gradient method
  • hybrid conjugate gradient method


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