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.