A descent nonlinear conjugate gradient method for large-scale unconstrained optimization

In this paper, a new nonlinear conjugate gradient method was proposed for large-scale unconstrained optimization which possesses the following three properties: (i) the sufficient descent property holds without any line searches; (ii) employing some steplength technique which ensures the Zoutendijk condition to be held, this method is globally convergent; (iii) this method inherits an important property of the Polak–Ribière–Polyak (PRP) method: the tendency to turn towards the steepest descent direction if a small step is generated away from the solution, preventing a sequence of tiny steps from happening. Preliminary numerical results show that this method is very promising.