2020/03/27 by Pedro Cisneros‐Velarde, Saber Jafarpour, Cisneros-Velarde, Pedro +3
Engineering · Mathematics · #34D23 #34H05 (Primary) #90C25 #93C95 (Secondary) #Control and Stability of Dynamical Systems #FOS: Computer and information sciences #FOS: Electrical engineering #G.1.6 #G.1.7 #Multiagent Systems (cs.MA) #Numerical methods for differential equations #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2003.12665
openalex publication_date 2020/03/27 · openalex created_date 2023/03/08 · openalex updated_date 2026/07/28
In this note, we provide an overarching analysis of primal-dual dynamics\nassociated to linear equality-constrained optimization problems using\ncontraction analysis. For the well-known standard version of the problem: we\nestablish convergence under convexity and the contracting rate under strong\nconvexity. Then, for a canonical distributed optimization problem, we use\npartial contractivity to establish global exponential convergence of its\nprimal-dual dynamics. As an application, we propose a new distributed solver\nfor the least-squares problem with the same convergence guarantees. Finally,\nfor time-varying versions of both centralized and distributed primal-dual\ndynamics, we exploit their contractive nature to establish bounds on their\ntracking error. To support our analyses, we introduce novel results on\ncontraction theory.\n