How can I find the distance from the edges of the polyhedron to the boundary of the ellipsoid?
The ellipsoid is parameterized by:
$$E = [ x : (x - x_c)^T H (x - x_c) \le m^2 ] $$
And it covers the polyhedron:
$$ P = [x : a_i^Tx \le b_i, i = 1,...,m] $$
Such that $P \subseteq E$