Minimum-Volume Covering Ellipsoids: Improving the Efficiency of the Wolfe-Atwood Algorithm for Large-Scale Instances by Pooling and Batching

Abstract

The Minimum-Volume Covering Ellipsoid (MVCE) problem is an important optimization problem that comes up in various areas of engineering and statistics. In this paper, we improve the state-of-the-art Wolfe-Atwood algorithm for solving the MVCE problem with pooling and batching procedures. This implementation yields significant improvements on the runtime of the algorithm for large-scale instances of the MVCE problem, which is demonstrated on quite extensive computational experiments.

Keywords

• minimum-volume covering ellipsoid
• Lowner-John ellipsoid
• large-scale optimization
• Wolfe-Atwood algorithm
• pooling
• batching