Related papers: Distributed alternating gradient descent for conve…
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 present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
In this paper, we investigate a distributed interval optimization problem which is modeled with optimizing a sum of convex interval-valued objective functions subject to global convex constraints, corresponding to agents over a time-varying…
Two distributed algorithms are described that enable all users connected over a network to cooperatively solve the problem of minimizing the sum of all users' objective functions over the intersection of all users' constraint sets, where…
This work concerns the analysis and design of distributed first-order optimization algorithms over time-varying graphs. The goal of such algorithms is to optimize a global function that is the average of local functions using only local…
This paper focuses on the distributed optimization of stochastic saddle point problems. The first part of the paper is devoted to lower bounds for the centralized and decentralized distributed methods for smooth (strongly) convex-(strongly)…
Solving optimization problems in multi-agent systems (MAS) involves information exchange between agents. These solutions must be robust to delays and errors that arise from an unreliable wireless network which typically connects the MAS. In…
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…
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…
Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments.…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
The paper addresses large-scale, convex optimization problems that need to be solved in a distributed way by agents communicating according to a random time-varying graph. Specifically, the goal of the network is to minimize the sum of…
We propose a divide-and-conquer (DAC) algorithm for constrained convex optimization over networks, where the global objective is the sum of local objectives attached to individual agents. The algorithm is fully distributed: each iteration…
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…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
We study structured convex optimization problems, with additive objective $r:=p + q$, where $r$ is ($\mu$-strongly) convex, $q$ is $L_q$-smooth and convex, and $p$ is $L_p$-smooth, possibly nonconvex. For such a class of problems, we…
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…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…