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...

The nonlinear conjugate gradient (CG) algorithm is a very effective method for optimization, especially for large-scale problems, because of its low memory requirement and simplicity. Zhang et al. (IMA J. Numer. Anal. 26:629-649, 2006) firstly propose a three-term CG algorithm based on the well known Polak-Ribière-Polyak (PRP) formula for unconstrained optimization, where their method has the s...

Recently, important contributions on convergence studies of conjugate gradient methods have been made by Gilbert and Nocedal [6]. They introduce a “sufficient descent condition” to establish global convergence results, whereas this condition is not needed in the convergence analyses of Newton and quasi-Newton methods, [6] hints that the sufficient descent condition, which was enforced by their ...

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