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

TL;DR

This paper introduces new algorithms for efficiently computing the minimum volume outer ellipsoid of the Minkowski sum of ellipsoids, improving runtime over existing semidefinite programming methods.

Contribution

The paper clarifies parameterizations, provides new optimality conditions, and proposes two novel algorithms for the parameterized MVOE computation.

Findings

Proposed algorithms run faster than existing SDP methods.

New analysis results on optimality conditions.

Connections among different parameterizations are clarified.

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.