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In this paper, we propose an inertial accelerated primal-dual method for thelinear equality constrained convex optimization problem. When the objectivefunction has a ``nonsmooth + smooth'' composite structure, we further proposean inexact inertial primal-dual method by linearizing the smooth individualfunction and solving the subproblem inexactly. Assuming merely convexity, weprove that the proposed methods enjoy $\mathcal{O}(1/k^2)$ convergence rate onthe objective residual and the feasibility violation in the primal model.Numerical results are reported to demonstrate the validity of the proposedmethods.

Inertial primal-dual methods for linear equality constrained convex optimization problems