Some Properties of A New Conjugate Gradient Method

It is proved that the new conjugate gradient method proposed by Dai and Yuan [5] produces a descent direction at each iteration for strictly convex problems. Consequently, the global convergence of the method can be established if the Goldstein line search is used. Further, if the function is uniformly convex, two Armijo-type line searches, the first of which is the standard Armijo line search, are also shown to guarantee the convergence of the new method.

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