In this paper we derive the efficiency 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 $O({1 \over k^3})$, where $k$ is the iteration counter. We derive also the efficiency estimate of a second-order scheme for smooth variational inequalities. Its global rate of convergence is established on the level $O({1 \over k})$.

## Citation

CORE Discussion Paper 2006/39, April 2006

## Article

View Cubic regularization of Newton's method for convex problems with constraints