Definitions
- A (polyhedral) cone in $\Bbb R^n$ is the solution set of a finite number of inequalities of the form $a_1x_1+\cdots+a_nx_n\geq 0$. Note that I don't require strict convexity, i.e. a cone $C$ is allowed to contain a positive-dimensional vector subspace of $\Bbb R^n$.
- A (polyhedral) fan $\Sigma$ in $\Bbb R^n$ is a set of cones which is (a) closed under taking faces and such that (b) if $C,D\in K$, then $C\cap D$ is a face of both $C$ and $D$.
Question
Given full knowledge of the defining inequalities of every cone in $\Sigma$, is there a known algorithm to determine whether the support $|\Sigma|:=\bigcup_{C\in \Sigma} C$ is convex?
