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

Ghania Hadji, Yamina Laskri, Tahar Bechouat, Rachid Benzine

Abstract


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 \(\beta_{k}^{HLB}\) as a convex combination of the Polak-Ribi\`{e}re-Polyak \(\left(
\beta _{k}^{PRP}\right) \left[ 1\right] \) and the Mohd Rivaie-Mustafa Mamat
and Abdelrhaman Abashar \(\left( \beta _{k}^{RMIL+}\right) \) i.e \(\beta
_{k}^{HLB}=\left( 1-\theta _{k}\right) \beta _{k}^{PRP}+\theta _{k}\beta
_{k}^{RMIL+}\). \ By comparing numerically CGHLB with PRP and RMIL+ and by using the Dolan and More CPU performance, we deduce that CGHLB is more efficient.


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DOI: http://dx.doi.org/10.24193/subbmath.2024.2.14

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