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)
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.
|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|
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