Inertial accelerated primal-dual algorithms for non-smooth convex optimization problems with linear equality constraints

Abstract: This paper is devoted to the study of an inertial accelerated primal-dual algorithm, which is based on a second-order differential system with time scaling, for solving a non-smooth convex optimization problem with linear equality constraints. We first introduce a second-order differential system with time scaling associated with the non-smooth convex optimization problem, and then obtain fast convergence rates for the primal-dual gap, the feasibility violation, and the objective residual along the trajectory generated by this system. Subsequently, based on the setting of the parameters involved, we propose an inertial accelerated primal-dual algorithm from the time discretization of this system. We also establish fast convergence rates for the primal-dual gap, the feasibility violation, and the objective residual. Furthermore, we demonstrate the efficacy of the proposed algorithm through numerical experiments.