Zobrazeno 1 - 10
of 278
pro vyhledávání: '"Davydov, Alexander A."'
In this letter, we study the proximal gradient dynamics. This recently-proposed continuous-time dynamics solves optimization problems whose cost functions are separable into a nonsmooth convex and a smooth component. First, we show that the cost func
Externí odkaz:
http://arxiv.org/abs/2409.10664
Autor:
Davydov, Alexander, Bullo, Francesco
Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction theory. These o
Externí odkaz:
http://arxiv.org/abs/2404.11707
Autor:
Davydov, Alexander, Bullo, Francesco
In this letter, we investigate sufficient conditions for the exponential stability of LTI systems driven by controllers derived from parametric optimization problems. Our primary focus is on parametric projection controllers, namely parametric progra
Externí odkaz:
http://arxiv.org/abs/2403.08159
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 equi
Externí odkaz:
http://arxiv.org/abs/2403.07572
Global stability and robustness guarantees in learned dynamical systems are essential to ensure well-behavedness of the systems in the face of uncertainty. We present Extended Linearized Contracting Dynamics (ELCD), the first neural network-based dyn
Externí odkaz:
http://arxiv.org/abs/2402.08090
In the literature, lines of the projective space $\mathrm{PG}(3,q)$ are partitioned into classes, each of which is a union of line orbits under the stabilizer group of the twisted cubic. The least studied class is named $\mathcal{O}_6$. This class co
Externí odkaz:
http://arxiv.org/abs/2401.00333
We propose and analyze a continuous-time firing-rate neural network, the positive firing-rate competitive network (\pfcn), to tackle sparse reconstruction problems with non-negativity constraints. These problems, which involve approximating a given i
Externí odkaz:
http://arxiv.org/abs/2311.03821
The length function $\ell_q(r,R)$ is the smallest possible length $n$ of a $ q $-ary linear $[n,n-r]_qR$ code with codimension (redundancy) $r$ and covering radius $R$. Let $s_q(N,\rho)$ be the smallest size of a $\rho$-saturating set in the projecti
Externí odkaz:
http://arxiv.org/abs/2310.02715
In this letter, we study distributed optimization and Nash equilibrium-seeking dynamics from a contraction theoretic perspective. Our first result is a novel bound on the logarithmic norm of saddle matrices. Second, for distributed gradient flows bas
Externí odkaz:
http://arxiv.org/abs/2309.05873
In this article, we provide a novel and broadly-applicable contraction-theoretic approach to continuous-time time-varying convex optimization. For any parameter-dependent contracting dynamics, we show that the tracking error is asymptotically proport
Externí odkaz:
http://arxiv.org/abs/2305.15595