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

Authors:
S. Damla Ahipasaoglu;Peng Sun;Michael J. Todd
Affiliations:
School of Operations Research and Industrial Engineering, Cornell University, Ithaca, USA;Fuqua School of Business, Duke University, Durham, USA;School of Operations Research and Industrial Engineering, Cornell University, Ithaca, USA
Venue:
Optimization Methods & Software
Year:
2008

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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.