-

 

 

 




Optimization Online





 

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

Yurii Nesterov (nesterov***at***core.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: 04/13/2006
Entry Accepted: 04/13/2006
Entry Last Modified: 04/13/2006

Modify/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
Mathematical Programming Society