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. By comparing numerically CGHLB with PRP and RMIL+ and by using the Dolan and More CPU performance, we deduce that CGHLB is more efficient. Keywords: Unconstrained optimization, hybrid conjugate gradient method, line search, descent property, global convergence.