✦ LIBER ✦
Positive semidefinite matrix completions on chordal graphs and constraint nondegeneracy in semidefinite programming
✍ Scribed by Houduo Qi
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 179 KB
- Volume
- 430
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
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.