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For $n$ real variables $x_1, \ldots, x_n$, I have a bunch of inequalities of form $2 x_i > x_j + x_k$ or $2 x_i < x_j + x_k$, where $i,j,k$ are distinct. My goal is to determine whether this set ...

I am looking for sufficient conditions such that a system of linear inequalities of the type $A x >0$ admits a non-negative solution $x \in \mathbb{R}^n_+$. I know a few properties of the $m \times ...