Ahipasaoglu, Selin Damla and Todd, Michael J. (2011) A modified Frank–Wolfe algorithm for computing minimum-area enclosing ellipsoidal cylinders: theory and algorithms. Computational geometry, Online . ISSN 0925-7721 (In Press)
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.
| Item Type: | Article |
|---|---|
| Official URL: | http://www.journals.elsevier.com/computational-geo... |
| Additional Information: | © 2011 Elsevier B.V. |
| Uncontrolled Keywords: | ISI, d-optimality, dk -optimality, Frank-Wolfe algorithm, linear convergence, minimum-area cylinders, minimum-volume ellipsoids |
| Library of Congress subject classification: | Q Science > QA Mathematics |
| Sets: | Research centres and groups > Management Science Group |
| Rights: | http://www.lse.ac.uk/library/rights/LSERO.htm |
| URL: | http://eprints.lse.ac.uk/40088/ |
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