## A lower bound on the optimal self-concordance parameter of convex cones

Let $K \subset \mathbb R^n$ be a regular convex cone, let $e_1,\dots,e_n \in \partial K$ be linearly independent points on the boundary of a compact affine section of the cone, and let $x^* \in K^o$ be a point in the relative interior of this section. For $k = 1,\dots,n$, let $l_k$ be the line through … Read more