Newton's method for computing the nearest correlation matrix with a simple upper bound
type: Item
instance of: scholarly article
title: Newton's method for computing the nearest correlation matrix with a simple upper bound
zbMATH Open document ID: 1229.90118
author: Houduo Qi
author: Qing-Na Li
author: Dong-Hui Li
published in: Journal of Optimization Theory and Applications
publication date: 2011-01-19T00:00:00Z
review text: A semismooth Newton method is extended to the nearest correlation matrix problem with a simple upper bound. Unlike the original semismooth Newton method proposed by \textit{H. Qi} and \textit{D. Sun} [SIAM J. Matrix Anal. Appl. 28, No. 2, 360--385 (2006; Zbl 1120.65049)] for the unbounded nearest correlation matrix problem, constraint nondegeneracy does not always hold for the optimal solution and thereby the method may lose its quadratic convergence property. The primal nondegeneracy is shown to be equivalent to the positive definiteness of every generalized Hessian (in the sense of Clarke) of the dual objective function. The authors show a quadratic convergence result for a modified semismooth Newton algorithm by adding a perturbation term to the generalized Hessian. Extensive numerical experiments are included.
reviewed by: Satoshi Ito
Mathematics Subject Classification ID: 90C22
Mathematics Subject Classification ID: 49M15
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 5838836
zbMATH Keywords: semismooth Newton method
zbMATH Keywords: nearest correlation matrix
zbMATH Keywords: constraint nondegeneracy
zbMATH Keywords: quadratic convergence
describes a project that uses: PENNON
describes a project that uses: QSDP
MaRDI profile type: Publication
full work available at URL: s10957-010-9738-6
OpenAlex ID: W2088265206
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DOI: 10.1007/S10957-010-9738-6
description: scientific article; zbMATH DE number 5838836