  In this paper we present a new method for solving optimization problems
involving the sum of two proper, convex, lower semicontinuous functions, one of
which has Lipschitz continuous gradient. The proposed method has a hybrid
nature that combines the usual forward-backward and the generalized conditional
gradient method. We establish a convergence rate of $o(k^{-1/3})$ under mild
assumptions with a specific step-size rule and show an application to a total
variation parameter learning problem, which demonstrates its benefits in the
context of nonsmooth convex optimization.
