On Weakly Contracting Dynamics for Convex Optimization
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909204983316480 |
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| author | Centorrino, Veronica Davydov, Alexander Gokhale, Anand Russo, Giovanni Bullo, Francesco |
| author_facet | Centorrino, Veronica Davydov, Alexander Gokhale, Anand Russo, Giovanni Bullo, Francesco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07572 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Weakly Contracting Dynamics for Convex Optimization Centorrino, Veronica Davydov, Alexander Gokhale, Anand Russo, Giovanni Bullo, Francesco Optimization and Control Dynamical Systems 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. |
| title | On Weakly Contracting Dynamics for Convex Optimization |
| topic | Optimization and Control Dynamical Systems |
| url | https://arxiv.org/abs/2403.07572 |