A Coordinate Descent Primal-Dual Algorithm and Application to Distributed Asynchronous Optimization

Bianchi, Pascal; Hachem, Walid; Iutzeler, Franck

doi:10.1109/tac.2015.2512043

Cited by 119 publications

(116 citation statements)

References 42 publications

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“…A primal-dual perturbation approach is explored in the paper [117]. An asynchronous version of such algorithm class is provided in [118]. Augmented Lagrangian algorithms for directed gossip networks are analyzed in [119].…”

Section: Discussion and Referencesmentioning

confidence: 99%

Distributed Optimization for Smart Cyber-Physical Networks

Notarstefano¹,

Notarnicola²,

Camisa³

2019

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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.

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Section: Discussion and Referencesmentioning

confidence: 99%

Distributed Optimization for Smart Cyber-Physical Networks

Notarstefano¹,

Notarnicola²,

Camisa³

2019

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“…The details are available in Appendix II. We highlight that allowing the packet loss probability of each edge to be in general different, the partition-based R-ADMM still conforms to the stochastic PRS framework of [28], [17]. Remark 2: Note that we restrict our analysis to the case of synchronous communications and updates, with the aim of investigating the performance of the R-ADMM over faulty networks.…”

Section: Networkmentioning

confidence: 99%

“…∀i ∈ V, j ∈ N i with probability one. Proving Proposition 3 is achieved by showing that the randomized partition-based ADMM of Algorithm 2 conforms to the stochastic Peaceman-Rachford splitting introduced in [28], [17] which is provably convergent. The details are available in Appendix II.…”

Section: Networkmentioning

confidence: 99%

“…More specifically, works devoted to the study of asynchronous ADMM implementations can be found. Examples are [17], where convergence of the ADMM is shown when only a subset of coordinates is randomly updated at every time instant, and the recent [18], where a framework for asynchronous operations is proposed. Conversely, literature on robustness analysis of ADMM in the presence of faulty communication is still scarce and usually confined to specific setups such as [19], [20] where only bounded delays and a particular master-slave communication architecture are considered.…”

Section: Introductionmentioning

confidence: 99%

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A Partition-Based Implementation of the Relaxed ADMM for Distributed Convex Optimization over Lossy Networks

Bastianello

Carli

Schenato

et al. 2018

2018 IEEE Conference on Decision and Control (CDC)

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In this paper we propose a distributed implementation of the relaxed Alternating Direction Method of Multipliers algorithm (R-ADMM) for optimization of a separable convex cost function, whose terms are stored by a set of interacting agents, one for each agent. Specifically the local cost stored by each node is in general a function of both the state of the node and the states of its neighbors, a framework that we refer to as 'partition-based' optimization. This framework presents a great flexibility and can be adapted to a large number of different applications. We show that the partition-based R-ADMM algorithm we introduce is linked to the relaxed Peaceman-Rachford Splitting (R-PRS) operator which, historically, has been introduced in the literature to find the zeros of sum of functions. Interestingly, making use of non expansive operator theory, the proposed algorithm is shown to be provably robust against random packet losses that might occur in the communication between neighboring nodes. Finally, the effectiveness of the proposed algorithm is confirmed by a set of compelling numerical simulations run over random geometric graphs subject to i.i.d. random packet losses.

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“…DRAFT Another strand of the asynchronous distributed optimization literature is based on first order primal-dual schemes. The authors in [5], developed a randomized primal-dual optimization algorithm using the idea of stochastic coordinate descent and utilized it to solve the distributed optimization problem asynchronously. The proposed algorithm, DAPD, converges almost surely under the assumption of independent and identically distributed updates.…”

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confidence: 99%

A Fast Distributed Asynchronous Newton-Based Optimization Algorithm

Mansoori

Wei

2020

IEEE Trans. Automat. Contr.

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One of the most important problems in the field of distributed optimization is the problem of minimizing a sum of local convex objective functions over a networked system. Most of the existing work in this area focus on developing distributed algorithms in a synchronous setting under the presence of a central clock, where the agents need to wait for the slowest one to finish the update, before proceeding to the next iterate. Asynchronous distributed algorithms remove the need for a central coordinator, reduce the synchronization wait, and allow some agents to compute faster and execute more iterations. In the asynchronous setting, the only known algorithms for solving this problem could achieve either linear or sublinear rate of convergence. In this work, we built upon the existing literature to develop and analyze an asynchronous Newton-based method to solve a penalized version of the problem. We show that this algorithm guarantees almost sure convergence with global linear and local quadratic rate in expectation.Numerical studies confirm superior performance of our algorithm against other asynchronous methods.

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A Coordinate Descent Primal-Dual Algorithm and Application to Distributed Asynchronous Optimization

Cited by 119 publications

References 42 publications

Distributed Optimization for Smart Cyber-Physical Networks

Distributed Optimization for Smart Cyber-Physical Networks

A Partition-Based Implementation of the Relaxed ADMM for Distributed Convex Optimization over Lossy Networks

A Fast Distributed Asynchronous Newton-Based Optimization Algorithm

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