The new nonlinear spectral conjugate descent method is constructed by combining the spectral conjugate gradient method andconjugate descent method. This method generates descent direction dk. Under the strong Wolfe rule this method is globally convergent.This paper analyzed global convergence of this method using the modified Armijo line search. The result shows that the new nonlinearspectral conjugate descent method is globally convergent under the modified Armijo line search.
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