A modified PRP conjugate gradient method with Armijo line search for large-scale unconstrained optimization

A modified PRP conjugate gradient method is proposed in this paper based on the modified secant equation. The main properties of the new method are described as follows: (i) the parameter β
_k
has not only gradient value information but also function value information; (ii) β
_k
≥ 0, ∀ k; (iii) the search direction generated by the presented method possesses both the sufficient descent and trust region properties without carrying out any line search. Under some suitable assumptions, we establish the global convergence of the new method with Armijo line search. Finally, some preliminary numerical results show that the proposed method is promising and effective.