New primal-dual proximal algorithm for distributed optimization

Latafat, Puya; Stella, Lorenzo; Patrinos, Panagiotis

doi:10.1109/cdc.2016.7798551

Cited by 25 publications

(25 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An asynchronous version of the distributed ADMM algorithm is proposed in [114]. Primal-dual algorithms for constrained optimization over networks are given in [115,116]. A primal-dual perturbation approach is explored in the paper [117].…”

Section: Discussion and Referencesmentioning

confidence: 99%

Distributed Optimization for Smart Cyber-Physical Networks

Notarstefano¹,

Notarnicola²,

Camisa³

2019

View full text Add to dashboard Cite

The presence of embedded electronics and communication capabilities as well as sensing and control in smart devices has given rise to the novel concept of cyber-physical networks, in which agents aim at cooperatively solving complex tasks by local computation and communication. Numerous estimation, learning, decision and control tasks in smart networks involve the solution of large-scale, structured optimization problems in which network agents have only a partial knowledge of the whole problem. Distributed optimization aims at designing local computation and communication rules for the network processors allowing them to cooperatively solve the global optimization problem without relying on any central unit. The purpose of this survey is to provide an introduction to distributed optimization methodologies. Principal approaches, namely (primal) consensus-based, duality-based and constraint exchange methods, are formalized. An analysis of the basic schemes is supplied, and state-of-the-art extensions are reviewed.

show abstract

Section: Discussion and Referencesmentioning

confidence: 99%

Distributed Optimization for Smart Cyber-Physical Networks

Notarstefano¹,

Notarnicola²,

Camisa³

2019

View full text Add to dashboard Cite

show abstract

“…. = x m }, since ker( √ W ) = span(1) due to the connectivity of the graph G. We note that a similar idea of writing the Laplacian as a product of a matrix B and its transpose has been employed in [32] using the incidence matrix. Hz − b 2 2 +…”

Section: Problem Statementmentioning

confidence: 99%

A dual approach for optimal algorithms in distributed optimization over networks

Uribe

Lee

Gasnikov

et al. 2020

Optimization Methods and Software

View full text Add to dashboard Cite

We study the optimal convergence rates for distributed convex optimization problems over networks, where the objective is to minimize the sum m i=1 f i (z) of local functions of the nodes in the network. We provide optimal complexity bounds for four different cases, namely: the case when each function f i is strongly convex and smooth, the cases when it is either strongly convex or smooth and the case when it is convex but neither strongly convex nor smooth. Our approach is based on the dual of an appropriately formulated primal problem, which includes the underlying static graph that models the communication restrictions. Our results show distributed algorithms that achieve the same optimal rates as their centralized counterparts (up to constant and logarithmic factors), with an additional cost related to the spectral gap of the interaction matrix that captures the local communications of the nodes in the network. (2000) 90C25 · 90C30 · 90C60 · 90C35 This work is an extended version of the manuscript: Optimal Algorithms for Distributed Optimization arXiv:1712.00232 [1]. Mathematics Subject Classification

show abstract

“…1) for (19), however, we do not pursue this in this paper and focus on problem (1) for clarity of exposition and length considerations. One can verify that the operator defining the fixed-point iterations in the Vũ-Condat algorithm is given by (12) with H = P + K and S defined as follows:…”

Section: A Related Primal-dual Algorithmsmentioning

confidence: 99%

A New Randomized Block-Coordinate Primal-Dual Proximal Algorithm for Distributed Optimization

Latafat

Freris

Patrinos

2019

IEEE Trans. Automat. Contr.

Self Cite

View full text Add to dashboard Cite

This paper proposes TriPD, a new primal-dual algorithm for minimizing the sum of a Lipschitz-differentiable convex function and two possibly nonsmooth convex functions, one of which is composed with a linear mapping. We devise a randomized block-coordinate version of the algorithm which converges under the same stepsize conditions as the full algorithm. It is shown that both the original as well as the block-coordinate scheme feature linear convergence rate when the functions involved are either piecewise linear-quadratic, or when they satisfy a certain quadratic growth condition (which is weaker than strong convexity). Moreover, we apply the developed algorithms to the problem of multi-agent optimization on a graph, thus obtaining novel synchronous and asynchronous distributed methods. The proposed algorithms are fully distributed in the sense that the updates and the stepsizes of each agent only depend on local information. In fact, no prior global coordination is required. Finally, we showcase an application of our algorithm in distributed formation control.

show abstract

New primal-dual proximal algorithm for distributed optimization

Cited by 25 publications

References 22 publications

Distributed Optimization for Smart Cyber-Physical Networks

Distributed Optimization for Smart Cyber-Physical Networks

A dual approach for optimal algorithms in distributed optimization over networks

A New Randomized Block-Coordinate Primal-Dual Proximal Algorithm for Distributed Optimization

Contact Info

Product

Resources

About