  We present two modified versions of the primal-dual splitting algorithm
relying on forward-backward splitting proposed in \cite{vu} for solving
monotone inclusion problems. Under strong monotonicity assumptions for some of
the operators involved we obtain for the sequences of iterates that approach
the solution orders of convergence of O(1/n) and O(\omega^n), for $\omega \in
(0,1)$, respectively. The investigated primal-dual algorithms are fully
decomposable, in the sense that the operators are processed individually at
each iteration. We also discuss the modified algorithms in the context of
convex optimization problems and present numerical experiments in image
processing and support vector machines classification.
