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
1151-1164
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
February 2009
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), .
(doi:10.1016/j.laa.2008.10.010).
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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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
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Date deposited: 22 Mar 2010
Last modified: 16 Mar 2024 03:41
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