On the Parameterized Computation of Minimum Volume Outer Ellipsoid of Minkowski Sum of Ellipsoids

Abstract: We consider the problem of computing certain parameterized minimum volume outer ellipsoidal (MVOE) approximation of the Minkowski sum of a finite number of ellipsoids. We clarify connections among several parameterizations available in the literature, obtain novel analysis results regarding the conditions of optimality, and based on the same, propose two new algorithms for computing the parameterized MVOE. Numerical results reveal faster runtime for the proposed algorithms than the state-of-the-art semidefinite programming approach of computing the same.