On Weakly Contracting Dynamics for Convex Optimization
arxiv(2024)
摘要
We investigate the convergence characteristics of dynamics that are
globally weakly and locally strongly contracting. 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.
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