Add to ORKGWe 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 ...
International audienceIn this paper we construct new families of extremal copositive matrices in arb...
AbstractLet E be the set of symmetric matrices in which every entry is 0 or ±1 and each diagonal ent...
The copositive cone, and its dual the completely positive cone, have useful applications in optimisa...
International audienceWe provide a complete classification of the extreme rays of the 6 × 6 copositi...
International audienceIn this work we complement the description of the extreme rays of the 6 × 6 co...
In this work we complement the description of the extreme rays of the $6 \times 6$ copositive cone w...
We represent the ensemble of extremal copositive matrices A ∈ COP^n of the copositive cone as a disj...
AbstractWe give an explicit characterization of all extreme rays of the cone C5 of 5×5 copositive ma...
International audienceLet A be an element of the copositive cone C^n. A zero u of A is a nonzero non...
International audienceLet n≥5 and let u_1,…,u_n be nonnegative real n-vectors such that the indices ...
International audienceWe give an explicit characterization of all extreme rays of the cone C_5 of 5×...
International audienceLet $A \in {\cal C}^n$ be an extremal copositive matrix with unit diagonal. Th...
International audienceLet $A \in {\cal C}^n$ be an exceptional extremal copositive $n \times n$ matr...
Let n be an integer not smaller than 5 and let u1,...,un be nonnegative real n-vectors such that the...
Let $A$ be an element of the copositive cone $\copos{n}$. A zero $\vu$ of $A$ is a nonnegative vecto...
International audienceIn this paper we construct new families of extremal copositive matrices in arb...
AbstractLet E be the set of symmetric matrices in which every entry is 0 or ±1 and each diagonal ent...
The copositive cone, and its dual the completely positive cone, have useful applications in optimisa...
International audienceWe provide a complete classification of the extreme rays of the 6 × 6 copositi...
International audienceIn this work we complement the description of the extreme rays of the 6 × 6 co...
In this work we complement the description of the extreme rays of the $6 \times 6$ copositive cone w...
We represent the ensemble of extremal copositive matrices A ∈ COP^n of the copositive cone as a disj...
AbstractWe give an explicit characterization of all extreme rays of the cone C5 of 5×5 copositive ma...
International audienceLet A be an element of the copositive cone C^n. A zero u of A is a nonzero non...
International audienceLet n≥5 and let u_1,…,u_n be nonnegative real n-vectors such that the indices ...
International audienceWe give an explicit characterization of all extreme rays of the cone C_5 of 5×...
International audienceLet $A \in {\cal C}^n$ be an extremal copositive matrix with unit diagonal. Th...
International audienceLet $A \in {\cal C}^n$ be an exceptional extremal copositive $n \times n$ matr...
Let n be an integer not smaller than 5 and let u1,...,un be nonnegative real n-vectors such that the...
Let $A$ be an element of the copositive cone $\copos{n}$. A zero $\vu$ of $A$ is a nonnegative vecto...
International audienceIn this paper we construct new families of extremal copositive matrices in arb...
AbstractLet E be the set of symmetric matrices in which every entry is 0 or ±1 and each diagonal ent...
The copositive cone, and its dual the completely positive cone, have useful applications in optimisa...