8 problems

Let $\mathcal{S}_n$ be the real symmetric $n\times n$ matrices, and let $\operatorname{COP}_n$ denote the cone of copositive matrices. An into copositivity preserver is a linear ma…

Let $Q\in{\mathcal{CP}}^{n}$ be a rational matrix. A matrix $B\in{\mathcal{COP}}^{n}$ with $\langle B,Q\rangle<0$ certifies that $Q\notin{\mathcal{CP}}^{n}$, while a rational…

Let $G$ be a graph with stability number $\alpha(G)$, and let $A_G$, $I$, and $J$ denote its adjacency, identity, and all-ones matrices, respectively. Define … By the Motzkin–Strau…

Finite-termination conjecture. For $A\notin{\mathcal{CP}}^n$, Procedure with a suitable pivot rule in Step2(b) ends after finitely many iterations with a separating witness $W$.

Forbidden-subgraph characterization conjecture. The list of graphs in Theorem is a complete list of forbidden subgraphs for the property of being SPN.

Subdivision conjecture for $K_4$. Every subdivision of $K_4$ in which all six edges were subdivided, each at least once, is SPN.

Let $\mathcal{C}_n$ denote the cone of copositive matrices of order $n$, and let $\theta_{\max}(\mathcal{C}_n)$ be the maximal possible angle between two matrices in this cone. Hir…

Strict copositivity conjecture. Strict copositivity of $B$ should be sufficient to ensure that the system admits no nontrivial solution.