2020/03/27 by Pedro Cisneros‐Velarde, Pedro Cisneros-Velarde, Cisneros-Velarde, Pedro +4
Computer Science · 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) #acm:34D23 #acm:34H05 #acm:90C25 #acm:93C95 #cs.MA #cs.SY #eess.SY #electronic engineering #information engineering #msc:34D23 #msc:34H05 #msc:90C25 #msc:93C95
paper · pdf · doi:10.48550/arxiv.2003.12665
openalex publication_date 2020/03/27 · arxiv created 2021/06/19 · arxiv updated 2021/06/22 · openalex created_date 2023/03/08 · openalex updated_date 2026/07/28
In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis. For the well-known standard version of the problem: we establish convergence under convexity and the contracting rate under strong convexity. Then, for a canonical distributed optimization problem, we use partial contractivity to establish global exponential convergence of its primal-dual dynamics. As an application, we propose a new distributed solver for the least-squares problem with the same convergence guarantees. Finally, for time-varying versions of both centralized and distributed primal-dual dynamics, we exploit their contractive nature to establish bounds on their tracking error. To support our analyses, we introduce novel results on contraction theory.