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

By Selin Damla Ahipasaoglu and Michael J. Todd

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

Topics: QA Mathematics
Publisher: Elsevier
Year: 2013
DOI identifier: 10.1016/j.comgeo.2011.11.004
OAI identifier: oai:eprints.lse.ac.uk:40088
Provided by: LSE Research Online
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