On the convergence of a modified regularized Newton method for convex optimization with singular solutions

Authors:
Weijun Zhou;Xinlong Chen
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

Citing 6
Cited 0

Regularized Newton Methods for Convex Minimization Problems with Singular Solutions

Computational Optimization and Applications
Inverse Problem Theory and Methods for Model Parameter Estimation

Inverse Problem Theory and Methods for Model Parameter Estimation
On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption

Computing
Truncated regularized Newton method for convex minimizations

Computational Optimization and Applications
Global Convergence of a New Hybrid Gauss-Newton Structured BFGS Method for Nonlinear Least Squares Problems

SIAM Journal on Optimization
On the convergence of an inexact Newton-type method

Operations Research Letters

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper we propose a modified regularized Newton method for convex minimization problems whose Hessian matrices may be singular. The proposed method is proved to converge globally if the gradient and Hessian of the objective function are Lipschitz continuous. Under the local error bound condition, we first show that the method converges quadratically, which implies that @?x"k-x^*@? is equivalent to dist(x"k,X), where X is the solution set and x"k-x^*@?X. Then we in turn prove the cubic convergence of the proposed method under the same local error bound condition, which is weaker than nonsingularity.