A new spectral conjugate gradient method based on Armijo line search

Abstract：In order to construct a new spectral conjugate gradient method with better convergence, a new conjugate coefficientβSNkkSΝwas constructed acccording to the existing conjugate coefficientsβ^*_kandβRMIL+kkRΜΙL+, thus a new specttral conjugate gradient method was given.The new method could always generate a sufficiently declining search drection in each iteration by selecting proper spectral coefficient.This property had an advantage that it depended neither on the line search which has been used nor on the convexity of the objective function.By using Armijo line search, the global convergence of this method was proved under general assumptions.

Keyword：spectral conjugate gradient method;conjugate coefficient;Armijo line search;global convergence;