- Cubic regularization of Newton's method for convex problems with constraints Yurii Nesterov (nesterovcore.ucl.ac.be) Abstract: 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 $O({1 \over k})$. Keywords: Convex optimiation with constraints, Newton method, global complexity bounds, cubic regularization Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization ) Citation: CORE Discussion Paper 2006/39, April 2006 Download: [PDF]Entry Submitted: 04/13/2006Entry Accepted: 04/13/2006Entry Last Modified: 04/13/2006Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.