We develop a novel variant of the classical Frank-Wolfe algorithm, which we call spectral Frank-Wolfe, for convex optimization over a spectrahedron. The spectral Frank-Wolfe algorithm has a novel ingredient: it computes a few eigenvectors of the gradient and solves a small-scale subproblem in each iteration. Such a procedure overcomes the slow convergence of the classical Frank-Wolfe algorithm due to ignoring eigenvalue coalescence. We demonstrate that strict complementarity of the optimization…