A Modified Frank-Wolfe Alogorithm for Computing Minimum-Area Enclosing Ellipsoidal Cylinders: Theory and Algorithms
Ahipasaoglu, S. Damla; Todd, Michael J.
We study a first-order method to find the minimum cross-sectional area ellipsoidal cylinder containing a finite set of points. This problem arises in optimal design in statistics when one is interested in a subset of the parameters. We provide convex formulations of this problem and its dual, and analyze a method based on the Frank-Wolfe algorithm for their solution. Under suitable conditions on the behavior of the method, we establish global and local convergence properties. However, difficulties may arise when a certain submatrix loses rank, and we describe a technique for dealing with this situation.
Linear convergence; Frank-Wolfe algorithm; minimum-volume ellipsoids; minimum-volume cylinders