On Weakly Contracting Dynamics for Convex Optimization

Autor:	Centorrino, Veronica, Davydov, Alexander, Gokhale, Anand, Russo, Giovanni, Bullo, Francesco
Rok vydání:	2024
Předmět:	Mathematics - Optimization and Control Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	We analyze the convergence behavior of \emph{globally weakly} and \emph{locally strongly contracting} dynamics. Such dynamics naturally arise in the context of convex optimization problems with a unique minimizer. We show that convergence to the equilibrium is \emph{linear-exponential}, in the sense that the distance between each solution and the equilibrium is upper bounded by a function that first decreases linearly and then exponentially. As we show, the linear-exponential dependency arises naturally in certain dynamics with saturations. Additionally, we provide a sufficient condition for local input-to-state stability. Finally, we illustrate our results on, and propose a conjecture for, continuous-time dynamical systems solving linear programs. Comment: 16 pages, 4 Figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.07572 Zobrazit plný text záznamu View this record from Arxiv