  We propose a new primal-dual algorithmic framework for a prototypical
constrained convex optimization template. The algorithmic instances of our
framework are universal since they can automatically adapt to the unknown
Holder continuity degree and constant within the dual formulation. They are
also guaran- teed to have optimal convergence rates in the objective residual
and the feasibility gap for each Holder smoothness degree. In contrast to
existing primal-dual algorithms, our framework avoids the proximity operator of
the objective function. We instead leverage computationally cheaper,
Fenchel-type operators, which are the main workhorses of the generalized
conditional gradient (GCG)-type methods. In contrast to the GCG-type methods,
our framework does not require the objective function to be differentiable, and
can also process additional general linear inclusion constraints, while
guarantees the convergence rate on the primal problem
