  By time discretization of a second-order primal-dual dynamical system with
damping $\alpha/t$ where an inertial construction in the sense of Nesterov is
needed only for the primal variable, we propose a fast primal-dual algorithm
for a linear equality constrained convex optimization problem. Under a suitable
scaling condition, we show that the proposed algorithm enjoys a fast
convergence rate for the objective residual and the feasibility violation, and
the decay rate can reach $\mathcal{O}(1/k^{\alpha-1})$ at the most. We also
study convergence properties of the corresponding primal-dual dynamical system
to better understand the acceleration scheme. Finally, we report numerical
experiments to demonstrate the effectiveness of the proposed algorithm.
