By time discretization of a primal-dual dynamical system, we propose an
inexact primal-dual algorithm, linked to the Nesterov's acceleration scheme,
for the linear equality constrained convex optimization problem. We also
consider an inexact linearized primal-dual algorithm for the composite problem
with linear constrains. Under suitable conditions, we show that these
algorithms enjoy fast convergence properties. Finally, we study the convergence
properties of the primal-dual dynamical system to better understand the
accelerated schemes of the proposed algorithms. We also report numerical
experiments to demonstrate the effectiveness of the proposed algorithms