A globally convergent version of the Polak-Ribière conjugate gradient method

In this paper we propose a new line search algorithm that ensures global convergence of the Polak-Ribiere conjugate gradient method for the unconstrained minimization of nonconvex differentiable functions. In particular, we show that with this line search every limit point produced by the Polak-Ribiere iteration is a stationary point of the objective function. Moreover, we define adaptive rules for the choice of the parameters in a way that the...