An augmented Lagrangian dual approach for the H-weighted nearest correlation matrix problem

H. Qi, Defeng Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

33 Citations (Scopus)

Abstract

Higham (2002, IMA J. Numer. Anal., 22, 329-343) considered two types of nearest correlation matrix problems, namely the W-weighted case and the H-weighted case. While the W-weighted case has since been well studied to make several Lagrangian dual-based efficient numerical methods available, the H-weighted case remains numerically challenging. The difficulty of extending those methods from the W-weighted case to the H-weighted case lies in the fact that an analytic formula for the metric projection onto the positive semidefinite cone under the H-weight, unlike the case under the W-weight, is not available. In this paper we introduce an augmented Lagrangian dual-based approach that avoids the explicit computation of the metric projection under the H-weight. This method solves a sequence of unconstrained convex optimization problems, each of which can be efficiently solved by an inexact semismooth Newton method combined with the conjugate gradient method. Numerical experiments demonstrate that the augmented Lagrangian dual approach is not only fast but also robust. © The author 2010. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Original languageEnglish
Pages (from-to)491-511
Number of pages21
JournalIMA Journal of Numerical Analysis
Volume31
Issue number2
DOIs
Publication statusPublished - 1 Apr 2011
Externally publishedYes

Keywords

  • augmented Lagrangian
  • conjugate gradient method
  • nearest correlation matrix
  • semismooth Newton method

ASJC Scopus subject areas

  • Mathematics(all)
  • Computational Mathematics
  • Applied Mathematics

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