The initial convergence rate of adaptive methods for polyhedral approximation of convex bodies

The convergence rate at the initial stage is analyzed for a previously proposed class of asymptotically optimal adaptive methods for polyhedral approximation of convex bodies. Based on the results, the initial convergence rate of these methods can be evaluated for arbitrary bodies (including the case of polyhedral approximation of polytopes) and the resources sufficient for achieving optimal asymptotic properties can be estimated.