This paper presents a trust region subspace method for minimizing large-scale unconstrained problems. We choose a subspace that consists of some old directions which are invariable and some newest directions which are changed at each iteration. A restart technique is used when the old directions...

In this paper we suggest a cubic regularization for a Newton method as applied to unconstrained minimization problem. For this scheme we prove general convergence results. We analyze the behavior of this scheme on different problem classes, for which we get global and local worst-case complexity...