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Block relaxation and majorization methods for the nearest correlation matrix with factor structure

Block relaxation and majorization methods for the nearest correlation matrix with factor structure
Block relaxation and majorization methods for the nearest correlation matrix with factor structure
We propose two numerical methods, namely the alternating block relaxation method and the alternating majorization method, for the problem of nearest correlation matrix with factor structure, which is highly nonconvex. In the block relaxation method, the subproblem is of the standard trust region problem, which is solved by Steighaug’s truncated conjugate gradient method or by the exact trust region method. In the majorization method, the subproblem has a closed-form solution. We then apply the majorization method to the case where nonnegative factors are required. The numerical results confirm that the proposed methods work quite well and are competitive against the best available methods.
block relaxation methods, majorization methods, correlation matrix, factor structure
0926-6003
Li, Qingna
a189d836-f8f0-407b-9983-0a73bf8a214a
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Xiu, Naihua
8e84e128-101b-4b57-aa47-e6002470ae9d
Li, Qingna
a189d836-f8f0-407b-9983-0a73bf8a214a
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Xiu, Naihua
8e84e128-101b-4b57-aa47-e6002470ae9d

Li, Qingna, Qi, Houduo and Xiu, Naihua (2010) Block relaxation and majorization methods for the nearest correlation matrix with factor structure. Computational Optimization and Applications. (doi:10.1007/s10589-010-9374-y).

Record type: Article

Abstract

We propose two numerical methods, namely the alternating block relaxation method and the alternating majorization method, for the problem of nearest correlation matrix with factor structure, which is highly nonconvex. In the block relaxation method, the subproblem is of the standard trust region problem, which is solved by Steighaug’s truncated conjugate gradient method or by the exact trust region method. In the majorization method, the subproblem has a closed-form solution. We then apply the majorization method to the case where nonnegative factors are required. The numerical results confirm that the proposed methods work quite well and are competitive against the best available methods.

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More information

Published date: 2010
Keywords: block relaxation methods, majorization methods, correlation matrix, factor structure

Identifiers

Local EPrints ID: 181559
URI: https://eprints.soton.ac.uk/id/eprint/181559
ISSN: 0926-6003
PURE UUID: 3b971ab0-b7ad-41e6-b3f8-cd6fe4e8c41a
ORCID for Houduo Qi: ORCID iD orcid.org/0000-0003-3481-4814

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Date deposited: 18 Apr 2011 10:39
Last modified: 20 Jul 2019 00:57

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