Fast Distributed Gradient Methods

Jakovetić, Dušan; Xavier, João; Moura, J.M.F.

doi:10.1109/tac.2014.2298712

Cited by 574 publications

(551 citation statements)

References 30 publications

Supporting

Mentioning

542

Contrasting

Unclassified

Order By: Relevance

“…4 we have shown that the sequence (V ) ∈N is converging. Our remaining task, which is the main result of this paper, is to demonstrate that the limit of the sequence (V ) ∈N is equal to the optimal value of the centralized cost function (7).…”

Section: B Convergence Of Algorithmmentioning

confidence: 71%

“…Recent work in the field of multi-agent systems, particularly in the field of consensus, has seen a resurgence of interest in the area of distributed optimization; see for example [3], [4], [5], [6], [7], [8], [9] and the references therein. Much of this work assumes the existence of a global cost function decomposable into the sum of cost functions for each agent.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Distributed Optimization Algorithm for the Predictive Control of Smart Grids

Braun

Grüne

Kellett

et al. 2016

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

Abstract-In this paper, we present a hierarchical, iterative distributed optimization algorithm, and show that the algorithm converges to the solution of a particular global optimization problem. The motivation for the distributed optimization problem is the predictive control of a smart grid, in which the states of charge of a network of residential-scale batteries are optimally coordinated so as to minimize variability in the aggregated power supplied to/from the grid by the residential network. The distributed algorithm developed in this paper calls for communication between a central entity and an optimizing agent associated with each battery, but does not require communication between agents. The distributed algorithm is shown to achieve the performance of a large-scale centralized optimization algorithm, but with greatly reduced communication overhead and computational burden. A numerical case study using data from an Australian electricity distribution network is presented to demonstrate the performance of the distributed optimization algorithm.

show abstract

Section: B Convergence Of Algorithmmentioning

confidence: 71%

Section: Introductionmentioning

confidence: 99%

A Distributed Optimization Algorithm for the Predictive Control of Smart Grids

Braun

Grüne

Kellett

et al. 2016

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

show abstract

“…We establish the convergence rates of the expected optimality gap in the cost function (at any node ) of mD-NG and mD-NC, in terms of the number of per node gradient evaluations and the number of per-node communications , when the functions are convex and differentiable, with Lipschitz continuous and bounded gradients. We show that the modified methods achieve in expectation the same rates that the methods in [3] achieve on static networks, namely: mD-NG converges at rates and , while mD-NC has rates and , where is an arbitrarily small positive number. We explicitly give the convergence rate constants in terms of the number of nodes and the network statistics, more precisely, in terms of the quantity (See ahead paragraph with heading Notation.…”

Section: B Contributionsmentioning

confidence: 74%

“…For problem (1), [3], see also [14], [15], presents two distributed Nesterov-like gradient algorithms for static (non-random) networks, referred to as D-NG (Distributed Nesterov Gradient algorithm) and D-NC (Distributed Nesterov gradient with Consensus iterations).…”

Section: B Contributionsmentioning

confidence: 99%

See 1 more Smart Citation

Convergence Rates of Distributed Nesterov-Like Gradient Methods on Random Networks

Jakovetić

Xavier²,

Moura

2014

IEEE Trans. Signal Process.

Self Cite

View full text Add to dashboard Cite

Abstract-We consider distributed optimization in random networks where nodes cooperatively minimize the sum of their individual convex costs. Existing literature proposes distributed gradient-like methods that are computationally cheap and resilient to link failures, but have slow convergence rates. In this paper, we propose accelerated distributed gradient methods that 1) are resilient to link failures; 2) computationally cheap; and 3) improve convergence rates over other gradient methods. We model the network by a sequence of independent, identically distributed random matrices drawn from the set of symmetric, stochastic matrices with positive diagonals. The network is connected on average and the cost functions are convex, differentiable, with Lipschitz continuous and bounded gradients. We design two distributed Nesterov-like gradient methods that modify the D-NG and D-NC methods that we proposed for static networks. We prove their convergence rates in terms of the expected optimality gap at the cost function. Let and be the number of per-node gradient evaluations and per-node communications, respectively. Then the modified D-NG achieves rates and , and the modified D-NC rates and , where is arbitrarily small. For comparison, the standard distributed gradient method cannot do better than and , on the same class of cost functions (even for static networks). Simulation examples illustrate our analytical findings.

show abstract

Distributed convex optimization based on ADMM and belief propagation methods

Zhang

2020

Asian Journal of Control

View full text Add to dashboard Cite

We consider a distributed convex optimization problem in which a connected network of agents collaboratively seeks to minimize the sum of their local objective functions over a common decision variable. We propose a new distributed optimization method in the Alternating Direction Method of Multipliers (ADMM) framework, But our method combines the celebrated Belief Propagation(BP) algorithm and relaxation iteration method to achieve distributed optimization. Numerical simulation shows that our proposed algorithms have good convergence speed. We also discuss the trade‐off between the convergence rate and the required communication and computational complexities.

show abstract

Fast Distributed Gradient Methods

Cited by 574 publications

References 30 publications

A Distributed Optimization Algorithm for the Predictive Control of Smart Grids

A Distributed Optimization Algorithm for the Predictive Control of Smart Grids

Convergence Rates of Distributed Nesterov-Like Gradient Methods on Random Networks

Distributed convex optimization based on ADMM and belief propagation methods

Contact Info

Product

Resources

About