In Boyd & Vandenberghe's Convex Optimization, an algorithm for finding the maximum volume inscribed ellipsoid inside a convex polyhedron is given (page 414, section 8.4.2).
I would like to find the maximum volume inscribed ellipsoid inside a non-convex polyhedron. Does anyone know an extension to this algorithm that could do this?
(The alternative would be to calculate an convex inner approximation of the nonconvex polyhedron and apply the original algorithm to that approximation.)