A modified Frank-Wolfe algorithm for computing minimum-area enclosing ellipsoidal cylinders: theory and algorithms
A modified Frank-Wolfe 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 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-area cylinders, D-optimality, D-k-optimality
494-519
Ahipasaoglu, S. Damla
d69f1b80-5c05-4d50-82df-c13b87b02687
Todd, Michael J.
7ab02b74-2513-4d34-93cc-d8663756a46c
July 2013
Ahipasaoglu, S. Damla
d69f1b80-5c05-4d50-82df-c13b87b02687
Todd, Michael J.
7ab02b74-2513-4d34-93cc-d8663756a46c
Ahipasaoglu, S. Damla and Todd, Michael J.
(2013)
A modified Frank-Wolfe algorithm for computing minimum-area enclosing ellipsoidal cylinders: theory and algorithms.
COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 46 (5), .
(doi:10.1016/j.comgeo.2011.11.004).
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.
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e-pub ahead of print date: 15 November 2011
Published date: July 2013
Keywords:
Linear convergence, Frank-Wolfe algorithm, Minimum-volume ellipsoids, Minimum-area cylinders, D-optimality, D-k-optimality
Identifiers
Local EPrints ID: 443152
URI: http://eprints.soton.ac.uk/id/eprint/443152
ISSN: 0925-7721
PURE UUID: 55772b10-d2c4-4066-9dbe-102e679ae78e
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Date deposited: 12 Aug 2020 16:37
Last modified: 17 Mar 2024 04:03
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Author:
Michael J. Todd
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