In this paper we propose an accelerated version of the cubic regularization of Newton's method [6]. The original version, used for minimizing a convex function with Lipschitz-continuous Hessian, guarantees a global rate of convergence of order O(1/k exp.2), where k is the iteration counter. Our...

In this paper we derive effciency estimates of the regularized Newton's method as applied to constrained convex minimization problems and to variational inequalities. We study a one- step Newton's method and its multistep accelerated version, which converges on smooth convex problems as O( 1 k3...

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...