I'm considering the following problem.
Given a collection of $m$ ellipsoids in $R^n$, compute the maximum volume ellipsoid inscribed in their intersection.
In Boyd & Vandenberghe, Convex Optimization (section 8.4.2) this problem is listed as one of the few special cases of extremal ellipsoids 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?
Many thanks in advance.