Cubic regularization of Newton method and its global performance

Authors:
Yurii Nesterov;B. T. Polyak
Affiliations:
Center for Operations Research and Econometrics (CORE), Catholic University of Louvain (UCL), 34 voie du Roman Pays, 1348, Louvain-la-Neuve, Belgium;Institute of Control Science, Profsojuznaya 65, 117997, Moscow, Russia
Venue:
Mathematical Programming: Series A and B
Year:
2006

Citing 0
Cited 12

Modified Gauss-Newton scheme with worst case guarantees for global performance

Optimization Methods & Software
Primal-dual exterior point method for convex optimization

Optimization Methods & Software
Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares

SIAM Journal on Numerical Analysis
Computing Points that Satisfy Second Order Necessary Optimality Conditions for Unconstrained Minimization

SIAM Journal on Optimization
Functional brain imaging with M/EEG using structured sparsity in time-frequency dictionaries

IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Complexity bounds for second-order optimality in unconstrained optimization

Journal of Complexity
On the Complexity of Steepest Descent, Newton's and Regularized Newton's Methods for Nonconvex Unconstrained Optimization Problems

SIAM Journal on Optimization
A trust region algorithm with adaptive cubic regularization methods for nonsmooth convex minimization

Computational Optimization and Applications
On the Oracle Complexity of First-Order and Derivative-Free Algorithms for Smooth Nonconvex Minimization

SIAM Journal on Optimization
Updating the regularization parameter in the adaptive cubic regularization algorithm

Computational Optimization and Applications
Low-rank quadratic semidefinite programming

Neurocomputing
A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we provide theoretical analysis for a cubic regularization of Newton method as applied to unconstrained minimization problem. For this scheme, we prove general local convergence results. However, the main contribution of the paper is related to global worst-case complexity bounds for different problem classes including some nonconvex cases. It is shown that the search direction can be computed by standard linear algebra technique.