New Three-Term Conjugate Gradient Method with Exact Line Search


  • Nurul Hafawati Fadhilah Universiti Teknologi MARA
  • Mohd Rivaie Universiti Teknologi MARA
  • Fuziyah Ishak Universiti Teknologi MARA
  • Nur Idalisa Universiti Teknologi MARA



Conjugate Gradient (CG) methods have an important role in solving large
scale unconstrained optimization problems. Nowadays, the Three-Term CG method has
become a research trend of the CG methods. However, the existing Three-Term CG
methods could only be used with the inexact line search. When the exact line search
is applied, this Three-Term CG method will be reduced to the standard CG method.
Hence in this paper, a new Three-Term CG method that could be used with the exact
line search is proposed. This new Three-Term CG method satisfies the descent condition
using the exact line search. Performance profile based on numerical results show that
this proposed method outperforms the well-known classical CG method and some related
hybrid methods. In addition, the proposed method is also robust in term of number of
iterations and CPU time.




How to Cite

Fadhilah, N. H., Rivaie, M., Ishak, F., & Idalisa, N. (2020). New Three-Term Conjugate Gradient Method with Exact Line Search. MATEMATIKA, 36(3), 197–207.