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

1 ABSTRACT In this paper we propose a new line search algorithm that ensures global convergence of the Polak-Ribi ere conjugate gradient method for the unconstrained minimization of nonconvex diierentiable functions. In particular, we show that every limit point produced by the Polak-Ribi ere iteration is a stationary point of the objective function. Moreover, we prove that, asymptotically, the rst stationary point along the search direction can be accepted and that, under strong convexity assumptions, the known global convergence results can be reobtained as a special case. From a computational point of view, we may expect that an algorithm incorporating the stepsize acceptance rules proposed here will retain the same good features of the Polak-Ribi ere method, while avoiding pathological situations.