Fast primal–dual algorithm via dynamical system for a linearly constrained convex optimization problem. (December 2022)

• Record Type: Journal Article
• Authors: He, Xin; Hu, Rong; Fang, Ya-Ping
• Is Part Of: Automatica. Volume 146(2022)
• Publication Date: 2022-12
• Subjects: Linearly constrained convex optimization problem -- Primal–dual algorithm -- Inertial primal–dual dynamical system -- Convergence rate -- Nesterov's acceleration; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2022.110547
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: By time discretization of a second-order primal–dual dynamical system with damping α / 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 O ( 1 / k α − 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.