Fast primal-dual algorithms via dynamics for linearly constrained convex optimization problems.

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.