  We propose a variant of the classical conditional gradient method for sparse
inverse problems with differentiable measurement models. Such models arise in
many practical problems including superresolution, time-series modeling, and
matrix completion. Our algorithm combines nonconvex and convex optimization
techniques: we propose global conditional gradient steps alternating with
nonconvex local search exploiting the differentiable measurement model. This
hybridization gives the theoretical global optimality guarantees and stopping
conditions of convex optimization along with the performance and modeling
flexibility associated with nonconvex optimization. Our experiments demonstrate
that our technique achieves state-of-the-art results in several applications.
