An extension of the three-term conjugate gradient method proposed by Zhang et al. is suggested. Based on an eigenvalue analysis on the search direction matrix, it is shown that the method possesses the sufficient descent property, no matter whether the line search is exact or not as well as the objective function is convex or not. It is interesting that the method can be considered as a hybridization of the conjugate gradient methods proposed by Zhang et al., and Hestenes and Stiefel. Global convergence of the method is established for uniformly convex objective functions. Comparative numerical results demonstrating efficiency of the proposed method are reported.

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