Journal article
The difference between 5 x 5 doubly nonnegative and completely positive matrices
Linear algebra and its applications, Vol.431(9), pp.1539-1552
10/01/2009
DOI: 10.1016/j.laa.2009.05.021
Abstract
The convex cone of n x n completely positive (CP) matrices and its dual cone of copositive matrices arise in several areas of applied mathematics, including optimization. Every CP matrix is doubly nonnegative (DNN), i.e., positive semidefinite and component-wise nonnegative, and it is known that, for n <= 4 only, every DNN matrix is CP. In this paper, we investigate the difference between 5 x 5 DNN and CP matrices. Defining a bad matrix to be one which is DNN but not CP, we: (i) design a finite procedure to decompose any n x n DNN matrix into the sum of a CP matrix and a bad matrix, which itself cannot be further decomposed; (ii) show that every bad 5 x 5 DNN matrix is the sum of a CP matrix and a single bad extreme matrix; and (iii) demonstrate how to separate bad extreme matrices from the cone of 5 x 5 CP matrices. (C) 2009 Elsevier Inc. All rights reserved.
Details
- Title: Subtitle
- The difference between 5 x 5 doubly nonnegative and completely positive matrices
- Creators
- Samuel Burer - University of IowaKurt M. Anstreicher - University of IowaMirjam Duer - University of Groningen
- Resource Type
- Journal article
- Publication Details
- Linear algebra and its applications, Vol.431(9), pp.1539-1552
- DOI
- 10.1016/j.laa.2009.05.021
- ISSN
- 0024-3795
- eISSN
- 1873-1856
- Publisher
- Elsevier
- Number of pages
- 14
- Grant note
- CCF-0545514 / NSF; National Science Foundation (NSF)
- Language
- English
- Date published
- 10/01/2009
- Academic Unit
- Industrial and Systems Engineering; Computer Science; Business Analytics
- Record Identifier
- 9984380533102771
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