An LMI description for the cone of Lorentz-positive maps II

Roland Hildebrand (roland.hildebrandimag.fr)

Abstract: Let L_n be the n-dimensional second order cone. A linear map from R^m to R^n is called positive if the image of L_m under this map is contained in L_n. For any pair (n,m) of dimensions, the set of positive maps forms a convex cone. We construct a linear matrix inequality of size (n-1)(m-1) that describes this cone.

Keywords: second order cone, semidefinite cone

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: Laboratory Jean Kuntzmann (LJK), University Joseph Fourier, Grenoble, France, August 2007

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Entry Submitted: 08/03/2007
Entry Accepted: 08/03/2007
Entry Last Modified: 10/07/2008

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