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In this paper, we propose a new framework to study distributed optimization problems with stochastic gradients by employing a multi-agent system with continuous-time dynamics. Here the goal of the agents is to cooperatively minimize the sum…
This paper considers the distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of local cost functions by using local information exchange. We first consider a distributed first-order primal-dual…
This paper studies a distributed multi-agent convex optimization problem. The system comprises multiple agents in this problem, each with a set of local data points and an associated local cost function. The agents are connected to a…
The non-smooth finite-sum minimization is a fundamental problem in machine learning. This paper develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying…
This paper considers a distributed convex optimization problem with inequality constraints over time-varying unbalanced digraphs, where the cost function is a sum of local objectives, and each node of the graph only knows its local…
In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and…
We present a distributed proximal-gradient method for optimizing the average of convex functions, each of which is the private local objective of an agent in a network with time-varying topology. The local objectives have distinct…
Decentralized optimization has become a fundamental tool for large-scale learning systems; however, most existing methods rely on the classical Lipschitz smoothness assumption, which is often violated in problems with rapidly varying…
Distributed optimization often requires finding the minimum of a global objective function written as a sum of local functions. A group of agents work collectively to minimize the global function. We study a continuous-time decentralized…
This paper deals with linear algebraic equations where the global coefficient matrix and constant vector are given respectively, by the summation of the coefficient matrices and constant vectors of the individual agents. Our approach is…
We present a distributed solution to optimizing a convex function composed of several non-convex functions. Each non-convex function is privately stored with an agent while the agents communicate with neighbors to form a network. We show…
We consider a distributed multi-agent network system where the goal is to minimize a sum of convex objective functions of the agents subject to a common convex constraint set. Each agent maintains an iterate sequence and communicates the…
We develop a distributed algorithm for convex Empirical Risk Minimization, the problem of minimizing large but finite sum of convex functions over networks. The proposed algorithm is derived from directly discretizing the second-order…
We consider convex and nonconvex constrained optimization with a partially separable objective function: agents minimize the sum of local objective functions, each of which is known only by the associated agent and depends on the variables…
This paper presents a set of continuous-time distributed algorithms that solve unconstrained, separable, convex optimization problems over undirected networks with fixed topologies. The algorithms are developed using a Lyapunov function…
We study a standard distributed optimization framework where $N$ networked nodes collaboratively minimize the sum of their local convex costs. The main body of existing work considers the described problem when the underling network is…
In this article, we focus on solving a class of distributed optimization problems involving $n$ agents with the local objective function at every agent $i$ given by the difference of two convex functions $f_i$ and $g_i$…
In this paper, we study convex optimization problems where agents of a network cooperatively minimize the global objective function which consists of multiple local objective functions. Different from most of the existing works, the local…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We…