Finding Minimum Volume Circumscribing Ellipsoids Using Generalized Copositive Programming

We study the problem of finding Löwner–John ellipsoid (i.e., an with minimum volume that contains a given convex set). reformulate as generalized copositive program and use reformulation to derive tractable semidefinite programming approximations for instances where set is defined by affine quadratic inequalities. prove that, when underlying polytope, our method never provides higher than one obtained scaling maximum volume-inscribed ellipsoid. empirically demonstrate proposed generates high-quality solutions can be solved much faster solving optimality. Furthermore, we outperform existing approximation schemes in terms solution time quality. present applications obtain piecewise linear decision rule dynamic distributionally robust problems random recourse generate ellipsoidal reachable states dynamical system allowed controls polytope.