  Difference-of-convex (DC) optimization problems are shown to be equivalent to
the minimization of a Lipschitz-differentiable "envelope". A gradient method on
this surrogate function yields a novel (sub)gradient-free proximal algorithm
which is inherently parallelizable and can handle fully nonsmooth formulations.
Newton-type methods such as L-BFGS are directly applicable with a classical
linesearch. Our analysis reveals a deep kinship between the novel DC envelope
and the forward-backward envelope, the former being a smooth and
convexity-preserving nonlinear reparametrization of the latter.
