Skip to main content
Article thumbnail
Location of Repository

Newton’s method for computing the nearest correlation matrix with a simple upper bound

By Qingna Li, Donghui Li and Houduo Qi

Abstract

The standard nearest correlation matrix can be efficiently computed by exploiting a recent development of Newton’s method (Qi and Sun in SIAM J. Matrix Anal. Appl. 28:360–385, 2006). Two key mathematical properties, that ensure the efficiency of the method, are the strong semismoothness of the projection operator onto the positive semidefinite cone and constraint nondegeneracy at every feasible point. In the case where a simple upper bound is enforced in the nearest correlation matrix in order to improve its condition number, it is shown, among other things, that constraint nondegeneracy does not always hold, meaning Newton’s method may lose its quadratic convergence. Despite this, the numerical results show that Newton’s method is still extremely efficient even for large scale problems. Through regularization, the developed method is applied to semidefinite programming problems with simple bounds

Topics: QA, QC
Year: 2010
OAI identifier: oai:eprints.soton.ac.uk:181535
Provided by: e-Prints Soton
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://dx.doi.org/10.1007/s109... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.