Comments on a new class of nonlinear conjugate gradient coefficients with global convergence properties

Abstract

In Rivaie et al [M. Rivaie, M. Mustafa, L.W. June and I. Mohd, A new class of nonlinear conjugate gradient coefficient with global convergence properties, Appl. Math. Comp, 218(2012), 11323-11332], an efficient CG algorithm has been proposed for solving unconstrained optimization problems. However, due to a wrong inequality (3.3) used in Rivaie et al., the proof of theorem 2 and the global convergence theorem 3 are not correct. We present the necessary corrections, then the proposed method in Rivaie et al still converges globally. Finally, we report some numerical comparisons.

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