A modified FrankWolfe algorithm for computing minimum-area enclosing ellipsoidal cylinders: Theory and algorithms
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 FrankWolfe 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.
frankwolfe algorithm linear convergence minimum-volume ellipsoids minimum-area cylinders d-optimality dk d k -optimality dk d k dk d k d k