Given a collection of $m$ ellipsoids in $\Bbb R^n$, compute the maximum volume ellipsoid inscribed in their intersection.
In section 8.4.2 of Boyd & Vandenberghe's Convex Optimization, this problem is listed as one of the few special cases of extremal ellipsoid problems that can be solved efficiently. However, I'm struggling to find a reference with an explicit bound on the running time. Are you aware of any such result? Could you please point me out some specific reference?