  We introduce and investigate the convergence properties of an inertial
forward-backward-forward splitting algorithm for approaching the set of zeros
of the sum of a maximally monotone operator and a single-valued monotone and
Lipschitzian operator. By making use of the product space approach, we expand
it to the solving of inclusion problems involving mixtures of linearly composed
and parallel-sum type monotone operators. We obtain in this way an inertial
forward-backward-forward primal-dual splitting algorithm having as main
characteristic the fact that in the iterative scheme all operators are accessed
separately either via forward or via backward evaluations. We present also the
variational case when one is interested in the solving of a primal-dual pair of
convex optimization problems with intricate objective functions.
