Behavior of the combination of PRP and HZ methods for unconstrained optimization

To achieve a conjugate gradient method which is strong in theory and efficient practice for solving unconstrained optimization problem, we propose hybridization of the Hager Zhang (HZ) Polak-Ribière Polyak (PRP) methods possesses an important property well known PRP method: tendency to turn towards steepest descent direction if small step generated away from solution, averting sequence tiny steps happening, new scalar \begin{document}$ \beta_k $\end{document} obtained by convex combination HZ under wolfe line search prove sufficient global convergence. Numerical results are reported show effectiveness our procedure.