  We propose a primal-dual algorithm with scaling, linked to the Nesterov's
acceleration scheme, for a linear equality constrained convex optimization
problem. We also consider two variants of the algorithm: an inexact proximal
primal-dual algorithm and an inexact linearized primal-dual algorithm. We prove
that these algorithms enjoy fast convergence properties, even faster than
$\mathcal{O}(1/k^2)$ under suitable scaling conditions. Finally, we study an
inertial primal-dual dynamic with time scaling for a better understanding of
accelerated schemes of the proposed algorithms.
