Suppose that $\{L_i\}$ is a collection of $k$ linear forms on $\mathbf R^n$. Let $$C=\{x \in \mathbf R^n : L_i \cdot x \geq 0 \text { for all } i \}$$
be the closed convex cone defined by the $\{L_i\}$.
What is the complexity, as a function of $k$, of finding the extremal rays of the cone $C$?