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The conjugate gradient method is one of the most effective algorithm for unconstrained nonlinear optimization problems. This is due to the fact that it does not need a lot of storage memory and its simple structure properties, which motivate us to propose a new hybrid conjugate gradient method through a convex combination of ${\beta }_k^{RMIL}$ and ${\beta }_k^{HS}$. We compute the convex parameter ${\theta }_k$ using the Newton direction. Global convergence is established through the strong Wolfe conditions. Numerical experiments show the...