New hybrid conjugate gradient method as a convex combination of PRP and RMIL+ methods.

The Conjugate Gradient (CG) method is a powerful iterative approach for solving large-scale minimization problems, characterized by its simplicity, low computation cost and good convergence. In this paper, a new hybrid conjugate gradient HLB method (HLB: Hadji-Laskri-Bechouat) is proposed and analysed for unconstrained optimization. We compute the parameter β_k^HLB as a convex combination of the Polak-Ribière-Polyak (β_k^PRP)[1] and the Mohd Rivaie-Mustafa Mamat and Abdelrhaman Abashar (β_k^RMIL+) i.e β_k^HLB=(1−θ_k)β_k^PRP+θ_kβ_k^RMIL+ . By comparing numerically CGHLB with PRP and RMIL+ and by using the Dolan and More CPU performance, we deduce that CGHLB is more efficient. [ABSTRACT FROM AUTHOR]