# Polyhedral annexation problem

Given a convex cone $LaTeX: C,$ a polytope $LaTeX: P$ contained in $LaTeX: C,$ and a compact, convex set $LaTeX: S$ with 0 in int$LaTeX: (S),$ find a point $LaTeX: y$ in $LaTeX: P\backslash S,$ or ascertain that $LaTeX: P$ is contained in $LaTeX: S.$