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On the non-homogeneity of completely positive cones

M. Seetharama Gowda(gowda***at***math.umbc.edu)
Roman Sznajder(rsznajder***at***bowiestate.edu)

Abstract: 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.

Keywords: completely positive cone, self-dual, irreducible, homogeneous

Category 1: Linear, Cone and Semidefinite Programming

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

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Entry Submitted: 05/10/2012
Entry Accepted: 05/10/2012
Entry Last Modified: 05/10/2012

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