A modified Frank-Wolfe algorithm for computing minimum-area enclosing ellipsoidal cylinders: Theory and algorithms

Authors:
S. Damla AhipaşAoğLu;Michael J. Todd
Affiliations:
Department of Management, Management Science Group, London School of Economics, Houghton Street, London WC2A 2AE, UK;Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, USA
Venue:
Computational Geometry: Theory and Applications
Year:
2013

Citing 6
Cited 0

Some comments of Wolfe's `away step'

Mathematical Programming: Series A and B
Trust-region methods

Trust-region methods
On cones of nonnegative quadratic functions

Mathematics of Operations Research
Convex Optimization

Convex Optimization
Computation of Minimum-Volume Covering Ellipsoids

Operations Research
Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids

Optimization Methods & Software

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.