The University of Southampton
University of Southampton Institutional Repository

A quadratically convergent Newton method for the nearest correlation matrix problem

A quadratically convergent Newton method for the nearest correlation matrix problem
A quadratically convergent Newton method for the nearest correlation matrix problem
The nearest correlation matrix problem is to find a correlation matrix which is closest to a given symmetric matrix in the Frobenius norm. The well-studied dual approach is to reformulate this problem as an unconstrained continuously differentiable convex optimization problem. Gradient methods and quasi-Newton methods such as BFGS have been used directly to obtain globally convergent methods. Since the objective function in the dual approach is not twice continuously differentiable, these methods converge at best linearly. In this paper, we investigate a Newton-type method for the nearest correlation matrix problem. Based on recent developments on strongly semismooth matrix valued functions, we prove the quadratic convergence of the proposed Newton method. Numerical experiments confirm the fast convergence and the high efficiency of the method.
correlation matrix, semismooth matrix equation, newton method, quadratic convergence
0895-4798
360-385
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Sun, Defeng
48acb796-0417-4d19-8be8-1739d44e50b0
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Sun, Defeng
48acb796-0417-4d19-8be8-1739d44e50b0

Qi, Houduo and Sun, Defeng (2006) A quadratically convergent Newton method for the nearest correlation matrix problem. SIAM Journal on Matrix Analysis and Applications, 28 (2), 360-385.

Record type: Article

Abstract

The nearest correlation matrix problem is to find a correlation matrix which is closest to a given symmetric matrix in the Frobenius norm. The well-studied dual approach is to reformulate this problem as an unconstrained continuously differentiable convex optimization problem. Gradient methods and quasi-Newton methods such as BFGS have been used directly to obtain globally convergent methods. Since the objective function in the dual approach is not twice continuously differentiable, these methods converge at best linearly. In this paper, we investigate a Newton-type method for the nearest correlation matrix problem. Based on recent developments on strongly semismooth matrix valued functions, we prove the quadratic convergence of the proposed Newton method. Numerical experiments confirm the fast convergence and the high efficiency of the method.

Text
2247305.pdf - Version of Record
Restricted to Repository staff only
Request a copy

More information

Published date: April 2006
Keywords: correlation matrix, semismooth matrix equation, newton method, quadratic convergence
Organisations: Operational Research

Identifiers

Local EPrints ID: 43246
URI: http://eprints.soton.ac.uk/id/eprint/43246
ISSN: 0895-4798
PURE UUID: 52289fbf-097d-40f6-aa0d-523e83a8deb9
ORCID for Houduo Qi: ORCID iD orcid.org/0000-0003-3481-4814

Catalogue record

Date deposited: 13 Jul 2007
Last modified: 14 Mar 2019 01:43

Export record

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×