You are required to read and agree to the below before accessing a full-text version of an article in the IDE article repository.

The full-text document you are about to access is subject to national and international copyright laws. In most cases (but not necessarily all) the consequence is that personal use is allowed given that the copyright owner is duly acknowledged and respected. All other use (typically) require an explicit permission (often in writing) by the copyright owner.

For the reports in this repository we specifically note that

  • the use of articles under IEEE copyright is governed by the IEEE copyright policy (available at
  • the use of articles under ACM copyright is governed by the ACM copyright policy (available at
  • technical reports and other articles issued by M‰lardalen University is free for personal use. For other use, the explicit consent of the authors is required
  • in other cases, please contact the copyright owner for detailed information

By accepting I agree to acknowledge and respect the rights of the copyright owner of the document I am about to access.

If you are in doubt, feel free to contact

Active Set Strategies for the Computation of Minimum-Volume Enclosing Ellipsoids



Linus Källberg, Daniel Andrén

Publication Type:

Report - MRTC


Mälardalen Real-Time Research Centre, Mälardalen University




We describe and evaluate several variants of an active set algorithm for the problem of computing a (1+ε)-approximation to the minimum-volume ellipsoid enclosing a given point set. The general approach is to run an existing algorithm repeatedly on smaller subsets of the points, and thereby achieve improved solution times compared to solving the whole problem directly. As the underlying algorithm, we use that of Todd and Yıldırım, which belongs to a group of algorithms based on the first-order Frank–Wolfe method. We propose multiple strategies to choose a new active set in each iteration, including an improved version of an existing strategy by Sun and Freund. In addition, we develop a variation of the elimination heuristic by Harman and Pronzato, that eliminates input points more aggressively in each iteration and then checks correctness of the solution before returning it. When used to (1 + 10^-6)-approximate the minimum-volume ellipsoid enclosing sets of 10^6 points in 2 to 25 dimensions, the proposed techniques generate speedups up to 70× compared to our baseline.


author = {Linus K{\"a}llberg and Daniel Andr{\'e}n},
title = {Active Set Strategies for the Computation of Minimum-Volume Enclosing Ellipsoids},
month = {November},
year = {2019},
publisher = {M{\"a}lardalen Real-Time Research Centre, M{\"a}lardalen University},
url = {}