Les rayons extrêmes du cône copositif de taille 6x6

International audienceWe provide a complete classification of the extreme rays of the 6 × 6 copositive cone COP^6. We proceed via a coarse intermediate classification of the possible minimal zero support set of an exceptional extremal matrix A ∈ COP^6. To each such minimal zero support set we construct a stratified semi-algebraic manifold in the space of real symmetric 6 × 6 matrices S^6 , parameterized in a semi-trigonometric way, which consists of all exceptional extremal matrices A ∈ COP^6 having this minimal zero support set. Each semi-algebraic stratum is characterized by the supports of the minimal zeros u as well as the supports of the corresponding matrix-vector products Au. The analysis uses recently and newly developed methods that are applicable also to copositive matrices of arbitrary order