Another hybrid conjugate gradient method and its global convergence for unconstrained optimization

In this paper, a hybrid conjugate gradient method is proposed for solving unconstrained optimization problems. The parameter β_k is computed as a convex combination of β_k^PRP and β*_k algorithms. The parameter θ_k is computed in such a way so that the direction corresponding to the conjugate gradient algorithm to be the Quasi-Newton equation. It is sufficient descent at every iteration. The theoretical analysis shows that the algorithm is global convergence under some suitable conditions. Numerical results show that this new algorithm is effective in unconstrained optimization problems.