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

arXiv: https://arxiv.org/abs/1803.08157 · HTML: https://mlsanity.com/paper/1803.08157/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2018.

## Built on by (most cited first, 4 of 4)

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- [Uncertainty-Aware Predictive Safety Filters for Probabilistic Neural Network Dynamics](https://mlsanity.com/paper/2604.26836/) (2026)
- [Convex and Nonconvex Sublinear Regression with Application to Data-driven Learning of Reach Sets](https://mlsanity.com/paper/2210.01919/) (2022)
- [Neural Network-assisted Interval Reachability for Systems with Control Barrier Function-Based Safe Controllers](https://mlsanity.com/paper/2504.08249/) (2025)

## Abstract (arXiv)

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.