  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.
