Computing the Maximum Volume Inscribed Ellipsoid of a Polytopic Projection

Abstract

This paper introduces a method for computing the maximum volume inscribed ellipsoid and k-ball of a projected polytope. It is known that deriving an explicit description of a projected polytope is NP-hard. By using adjustable robust optimization techniques, we construct a computationally tractable method that does not require an explicit description of the projection. The obtained centers of the projected polytope are considered as the robust solutions, e.g., for design centering problems. We perform numerical experiments on a simple polytope and a color tube design problem. The color tube design problem demonstrates that the obtained solutions are much more robust than the nominal approach with a slight compromise on the objective value. Some other potential applications include ellipsoidal approximations to polytopic sets, nominal scenario recovery, and cutting-plane method.