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 beta HLB k as a convex combination of the Polak-Ribiere-Polyak ( beta(P RP )(k))and the Mohd Rivaie-Mustafa Mamat and Abdelrhaman Abashar (beta(k) (RMIL +) ) i.e. beta (HLB)(k ) = (1 - theta (k) ) beta(P RP)(k) + theta (k) beta(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.