2024/03/12 by Centorrino, Veronica, Davydov, Alexander, Gokhale, Anand +2 · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2403.07572
We analyze the convergence behavior of globally weakly and 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 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.