Global Convergence of Two Spectral Conjugate Gradient Methods for Unconstrained Optimization

Spectral conjugate gradient method contains two directions regulatory parameters is a kind of method for unconstrained optimization that combines conjugate gradient method with spectral gradient method.In this paper,based on the new conjugate parameters and spectral parameters,two spectral conjugate gradient methods are proposed;the corresponding methods are equivalent to the FR conjugate gradient method when the line search is exact.Moreover,the global convergence of algorithm 1with Wolfe line search is proved,the global convergence of algorithm 2 with standard Armijo line search is proved.The given numerical results show that the new methods are efficient.