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Positive semidefinite matrix completions on chordal graphs and constraint nondegeneracy in semidefinite programming

Positive semidefinite matrix completions on chordal graphs and constraint nondegeneracy in semidefinite programming
Positive semidefinite matrix completions on chordal graphs and constraint nondegeneracy in semidefinite programming
Let G=(V,E) be a graph. In matrix completion theory, it is known that the following two conditions are equivalent: (i) G is a chordal graph; (ii) Every G-partial positive semidefinite matrix has a positive semidefinite matrix completion. In this paper, we relate these two conditions to constraint nondegeneracy condition in semidefinite programming and prove that they are each equivalent to (iii) For any G-partial positive definite matrix that has a positive semidefinite completion, constraint nondegeneracy is satisfied at each of its positive semidefinite matrix completions
chordal graph, constraint nondegeneracy, matrix completion, semidefinite programming
0024-3795
1151-1164
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85

Qi, Houduo (2009) Positive semidefinite matrix completions on chordal graphs and constraint nondegeneracy in semidefinite programming. Linear Algebra and Its Applications, 430 (4), 1151-1164. (doi:10.1016/j.laa.2008.10.010).

Record type: Article

Abstract

Let G=(V,E) be a graph. In matrix completion theory, it is known that the following two conditions are equivalent: (i) G is a chordal graph; (ii) Every G-partial positive semidefinite matrix has a positive semidefinite matrix completion. In this paper, we relate these two conditions to constraint nondegeneracy condition in semidefinite programming and prove that they are each equivalent to (iii) For any G-partial positive definite matrix that has a positive semidefinite completion, constraint nondegeneracy is satisfied at each of its positive semidefinite matrix completions

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More information

Published date: February 2009
Keywords: chordal graph, constraint nondegeneracy, matrix completion, semidefinite programming
Organisations: Operational Research

Identifiers

Local EPrints ID: 54530
URI: http://eprints.soton.ac.uk/id/eprint/54530
ISSN: 0024-3795
PURE UUID: 3fbce8f2-1a96-46cd-90b4-92afb2d82c14
ORCID for Houduo Qi: ORCID iD orcid.org/0000-0003-3481-4814

Catalogue record

Date deposited: 22 Mar 2010
Last modified: 09 Jan 2022 03:17

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