AN IMPROVED CHARACTERISATION OF THE INTERIOR OF THE COMPLETELY POSITIVE CONE
By Peter J. C. Dickinson. 2010
65 citations recorded by the source corpus.
A symmetric matrix is defined to be completely positive if it allows a factorisa- tion BB T , where B is an entrywise nonnegative matrix. This set is useful in certain optimisation problems. The interior of the completely positive cone has previously been characterised by Dur and Still (M. Dur and G. Still, Interior points of the completely positive cone, Electronic Journal of Linear Algebra, 17:48-53, 2008). In this paper, we introduce the concept of the set of zeros in the nonnegative orthant for a quadratic form, and use the properties of this set to give a more relaxed characterisation of the interior of the completely positive cone.
Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/3451473a3d7b5a2ea8fb0640a42c68b8ccbf7fdf
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In Computational Theory and Mathematics
In Electrical and Electronic Engineering
In Numerical Analysis
Citations in the corpus
- Irreducible elements of the copositive cone (2013, methodology): “This notation is similar to that used by Dickinson in [7], except we will exclude the vector 0 from the set.”
- Copositive Programming – a Survey (2010, background): “Dickinson [24] gave an improved characterization which reads as follows:”
- Geometry of the copositive and completely positive cones (2011, methodology): “In order to do this we first introduce the concept of the set of zeros in the nonnegative orthant for a quadratic form, as used previously in [18].”