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The paper is devoted to the study of the coneof copositive matrices. Based on the concept of immobile indices known from semi-infinite optimization, we define zero and minimal zero vectors of a subset of the coneand use them to obtain different representations of the faces ofand the corresponding dual cones. The minimal face ofcontaining a given convex subset of this cone is described, and some propositions are proved that allow obtaining equivalent descriptions of the feasible sets of copositive problems.

On equivalent representations and properties of faces of the cone of copositive matrices