The spectral conjugate gradient method is an important extension of the conjugate gradient method, and is one of the effective methods for solving large-scale unconstrained optimization. The designing for the spectral parameter is a critical work in spectral conjugate gradient method. In this paper, a new spectral parameter is given, and a new framework of spectral conjugate gradient method is established when the conjugate parameter satisfies a certain restrictive condition. Under the general assumptions and in case where the strong Wolfe inexact line search criterion to yield the step length, the new algorithm framework have sufficient descent property and global convergence. Finally, for the new algorithm framework, the existing conjugate parameter that satisfies the restrictive condition is selected, and the numerical experiments are done to compare the proposed algorithm with other potential algorithms, and the numerical results show that the established algorithm is promising.
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