Global convergence of a modified Hestenes‐Stiefel nonlinear conjugate gradient method with Armijo line search

In this article, based on the modified secant equation, we propose a modified Hestenes‐Stiefel (HS) conjugate gradient method which has similar form as the CG‐DESCENT method proposed by Hager and Zhang (2005). The presented method can generate sufficient descent directions without any line search. Under some mild conditions, we show that it is globally convergent with Armijo line search. Moreover, the R‐linear convergence rate of the modified HS method is established. Preliminary numerical results show that the proposed method is promising, and competitive with the well‐known CG‐DESCENT method.