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 Gulat and Marcotte. Computational tests confirm the attractive features of this method.