Related papers: Uniform-in-time propagation of chaos for consensus…
This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems…
This paper analyzes consensus in multi-agent systems under uniform and nonuniform communication delays, a key challenge in distributed coordination with applications to robotic swarms. It investigates the convergence of a consensus…
We address the problem of determining if a discrete time switched consensus system converges for any switching sequence and that of determining if it converges for at least one switching sequence. For these two problems, we provide…
We introduce a general mathematical framework for distributed algorithms, and a monotonicity property frequently satisfied in application. These properties are leveraged to provide finite-time guarantees for converging algorithms, suited…
In this paper we study Kac's 1D particle system, consisting of the velocities of $N$ particles colliding at constant rate and randomly exchanging energies. We prove uniform (in time) propagation of chaos in Wasserstein distance with…
We establish general conditions under which there exists uniform in time convergence between a stochastic process and its approximated system. These standardised conditions consist of a local in time estimate between the original and the…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
We study distributed convex optimization with two ubiquitous forms of coupling: consensus constraints and global affine equalities. We first design a linearized method of multipliers for the consensus optimization problem. Without…
We study a fixed step-size noisy distributed gradient descent algorithm for solving optimization problems in which the objective is a finite sum of smooth but possibly non-convex functions. Random perturbations are introduced to the…
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…
Most algorithms for decentralized learning employ a consensus or diffusion mechanism to drive agents to a common solution of a global optimization problem. Generally this takes the form of linear averaging, at a rate of contraction…
Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
Multilayer networks provide a more comprehensive framework for exploring real-world and engineering systems than traditional single-layer networks, consisting of multiple interacting networks. However, despite significant research in…
The trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation in the presence of a convex external potential, without smallness restriction on the interaction. From this are…
In this paper, the optimal consensus problem for general nonlinear multi-agent systems is studied, where both leaderless and leader-follower cases are considered in a unified framework. The key idea is to convert consensus problems into…
In this paper, uniform in time quantitative propagation of chaos in $L^1$-Wasserstein distance for mean field interacting particle system is derived, where the diffusion coefficient is allowed to be interacting and the drift is assumed to…
This paper fully studies distributed optimal consensus problem in non-directed dynamical networks. We consider a group of networked agents that are supposed to rendezvous at the optimal point of a collective convex objective function. Each…
In this paper, we consider the problem of containment control of multi-agent systems with multiple stationary leaders, interacting over a directed network. While, containment control refers to just ensuring that the follower agents reach…