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

Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids
Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids
We show the linear convergence of a simple first-order algorithm for the minimum-volume enclosing ellipsoid problem and its dual, the D-optimal design problem of statistics. Using similar techniques, we show the linear convergence of the Frank–Wolfe algorithm with away steps applied to the simplex, under conditions different from those of Guélat and Marcotte. Computational tests confirm the attractive features of this method.
linear convergence, Frank-Wolfe algorithm, Minimum-volume ellipsoids, optimizing on a simplex
1055-6788
5-19
Ahipasaoglu, S. Damla
d69f1b80-5c05-4d50-82df-c13b87b02687
Sun, Peng
41499e73-cc73-4703-b992-8a1200cfebd4
Todd, Michael J.
7ab02b74-2513-4d34-93cc-d8663756a46c
Ahipasaoglu, S. Damla
d69f1b80-5c05-4d50-82df-c13b87b02687
Sun, Peng
41499e73-cc73-4703-b992-8a1200cfebd4
Todd, Michael J.
7ab02b74-2513-4d34-93cc-d8663756a46c

Ahipasaoglu, S. Damla, Sun, Peng and Todd, Michael J. (2008) Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids. Optimization Methods and Software, 23 (1), 5-19. (doi:10.1080/10556780701589669).

Record type: Article

Abstract

We show the linear convergence of a simple first-order algorithm for the minimum-volume enclosing ellipsoid problem and its dual, the D-optimal design problem of statistics. Using similar techniques, we show the linear convergence of the Frank–Wolfe algorithm with away steps applied to the simplex, under conditions different from those of Guélat and Marcotte. Computational tests confirm the attractive features of this method.

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More information

Published date: February 2008
Keywords: linear convergence, Frank-Wolfe algorithm, Minimum-volume ellipsoids, optimizing on a simplex

Identifiers

Local EPrints ID: 443143
URI: http://eprints.soton.ac.uk/id/eprint/443143
ISSN: 1055-6788
PURE UUID: 7d68a08a-f3fd-4cb7-aeb6-c94074d41d78
ORCID for S. Damla Ahipasaoglu: ORCID iD orcid.org/0000-0003-1371-315X

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Date deposited: 12 Aug 2020 16:32
Last modified: 18 Feb 2021 17:42

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Contributors

Author: Peng Sun
Author: Michael J. Todd

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