A modified Frank-Wolfe algorithm for computing minimum-area enclosing ellipsoidal cylinders: Theory and algorithms
نویسندگان
چکیده
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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عنوان ژورنال:
- Comput. Geom.
دوره 46 شماره
صفحات -
تاریخ انتشار 2013