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

Roland Hildebrand (1)

1 CASYS - Calculs Algébriques et Systèmes Dynamiques

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.

Mots clés: second-order cone; semidefinite cone

Domaines: Optimisation et contrôle [math.OC]

Roland Hildebrand. An LMI description for the cone of Lorentz-positive maps II. Linear and Multilinear Algebra, 2011, 59 (7), pp.719-731. ⟨10.1080/03081087.2010.486243⟩. ⟨hal-00765665⟩