FIRST-ORDER METHODS FOR THE IMPATIENT: SUPPORT IDENTIFICATION IN FINITE TIME WITH CONVERGENT FRANK-WOLFE VARIANTS

In this paper, we focus on the problem of minimizing a nonconvex function over the unit simplex. We analyze two well-known and widely used variants of the Frank-Wolfe algorithm and first prove global convergence of the iterates to stationary points, both when using exact and Armijo line search. Then we show that the algorithms identify the support in a finite number of iterations (the identification result does not hold for the classic Frank-Wolfe algorithm). This, to the best of our knowledge, is the first time a manifold identification property has been shown for such a class of methods.