Newton's Method for Computing the Nearest Correlation Matrix with a Simple Upper Bound

Qingna Li, Donghui Li*, Houduo Qi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)546-568
Number of pages23
JournalJournal of Optimization Theory and Applications
Volume147
Issue number3
DOIs
Publication statusPublished - Dec 2010
Externally publishedYes

Keywords

  • Constraint nondegeneracy
  • Correlation matrix
  • Quadratic convergence
  • Semismooth Newton method

Fingerprint

Dive into the research topics of 'Newton's Method for Computing the Nearest Correlation Matrix with a Simple Upper Bound'. Together they form a unique fingerprint.

Cite this