A Modified Hestenes-Stiefel Conjugate Gradient Method and its Global convergence for unconstrained optimization

In this paper, we proposed a modified Hestenes-Stiefel (HS) conjugate gradient method. This achieves a high order accuracy in approximating the second order curvature information of the objective function by utilizing the modified secant condition which is proposed by Babaie-Kafaki [1], also we derive a nonquadratic conjugate gradient model. The important property of the suggestion method that is satisfy the descent property and global convergence independent of the accuracy of the line search. In addition, we prove the global convergence under some suitable conditions, and we reported the numerical results under these conditions.