Given a closed cone C in the Euclidean n-space, the completely positive cone of C is the convex cone K generated by matrices of the form uu^T as u varies over C. Examples of completely positive cones include the positive semidefinite cone (when C is the entire Euclidean n-space) and the cone of completely positive matrices (when C is the nonnegative orthant). Completely positive cones arise, for example, in the reformulation of a nonconvex quadratic minimization problem over an arbitrary set with linear and binary constraints as a conic linear program. This paper deals with the questions of when (or whether) K is self-dual, irreducible, and/or homogeneous.

## Citation

Technical Report trGOW11-04 Department of Mathematics and Statistics University of Maryland Baltimore County Baltimore, MD 21250 USA November, 2011