Global Convergence of a Modified Hestenes-Stiefel Conjugate Gradient Method under Armijo-type Line Search

A new modified Hestenes-Stiefel nonlinear conjugated gradient (MHSCG) algorithm was put forth. Under exact line search the new algorithm is standardized as an HS algorithm. The new algorithm characterized by its independence of the line search rules and a sufficient descent property under Armijo line search and is of good global convergence. Preliminary numerical results show that the method gives a better performance in contrast with algorithms like PRP, HS and LS.