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We consider the distributed optimization problem for the sum of convex functions where the underlying communications network connecting agents at each time is drawn at random from a collection of directed graphs. Building on an earlier work…
We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity…
In this work, we consider the problem of a network of agents collectively minimizing a sum of convex functions. The agents in our setting can only access their local objective functions and exchange information with their immediate…
This paper is devoted to distributed continuous-time and discrete-time optimization problems with nonuniform convex constraint sets and nonuniform stepsizes for general differentiable convex objective functions. The communication graphs are…
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, a distributed subgradient-based algorithm is proposed for continuous-time multi-agent systems to search a feasible solution to convex inequalities. The algorithm involves each agent achieving a state constrained by its own…
Many large-scale constrained optimization problems can be formulated as bilevel distributed optimization tasks over undirected networks, where agents collaborate to minimize a global cost function while adhering to constraints, relying only…
We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure…
The stochastic subgradient method is a widely-used algorithm for solving large-scale optimization problems arising in machine learning. Often these problems are neither smooth nor convex. Recently, Davis et al. [1-2] characterized the…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
The incremental aggregated gradient algorithm is popular in network optimization and machine learning research. However, the current convergence results require the objective function to be strongly convex. And the existing convergence…
We propose a new distributed optimization algorithm for solving a class of constrained optimization problems in which (a) the objective function is separable (i.e., the sum of local objective functions of agents), (b) the optimization…
We present a distributed optimization algorithm for solving online personalized optimization problems over a network of computing and communicating nodes, each of which linked to a specific user. The local objective functions are assumed to…
We propose a general scheme for solving convex and non-convex optimization problems on manifolds. The central idea is that, by adding a multiple of the squared retraction distance to the objective function in question, we "convexify" the…
This paper investigates solving convex composite optimization on an undirected network, where each node, privately endowed with a smooth component function and a nonsmooth one, is required to minimize the sum of all the component functions…
We consider unconstrained randomized optimization of convex objective functions. We analyze the Random Pursuit algorithm, which iteratively computes an approximate solution to the optimization problem by repeated optimization over a…
This paper proposes a fast decentralized algorithm for solving a consensus optimization problem defined in a directed networked multi-agent system, where the local objective functions have the smooth+nonsmooth composite form, and are…
In this paper, we develop a novel distributed algorithm for addressing convex optimization with both nonlinear inequality and linear equality constraints, where the objective function can be a general nonsmooth convex function and all the…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…