Fast Consensus by the Alternating Direction Multipliers Method

Erseghe, Tomaso; Zennaro, Davide; Dall’Anese, Emiliano; Vangelista, Lorenzo

doi:10.1109/tsp.2011.2162831

Cited by 139 publications

(140 citation statements)

References 29 publications

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“…In what comes next, we consider two alternatives that are commonly used in the literature (c.f., e.g. [14]). …”

Section: Problem Formulationmentioning

confidence: 99%

“…Each data point of the plot is the average of the convergence factors of 50 instances of the randomly generated graphs with the same number of nodes. In the edge-variable scenario, we compare the ADMM iterates to Fast-consensus [14] from the ADMM literature and two recent accelerated consensus schemes: Oreshkin et al [11] and Ghadimi et al [22]. These algorithms include a two-tap memory mechanism in which the values of two-last iterates are taken into account in computing the next iterate.…”

Section: Numerical Experimentsmentioning

confidence: 99%

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The ADMM algorithm for distributed averaging: Convergence rates and optimal parameter selection

Ghadimi

Teixeira

Rabbat

et al. 2014

2014 48th Asilomar Conference on Signals, Systems and Computers

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Abstract-We derive the optimal step-size and overrelaxation parameter that minimizes the convergence time of two ADMM-based algorithms for distributed averaging. Our study shows that the convergence times for given step-size and over-relaxation parameters depend on the spectral properties of the normalized Laplacian of the underlying communication graph. Motivated by this, we optimize the edge-weights of the communication graph to improve the convergence speed even further. The performance of the ADMM algorithms with our parameter selection are compared with alternatives from the literature in extensive numerical simulations on random graphs.

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“…In what comes next, we consider two alternatives that are commonly used in the literature (c.f., e.g. [14]). …”

Section: Problem Formulationmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

The ADMM algorithm for distributed averaging: Convergence rates and optimal parameter selection

Ghadimi

Teixeira

Rabbat

et al. 2014

2014 48th Asilomar Conference on Signals, Systems and Computers

View full text Add to dashboard Cite

show abstract

“…In the literature, there exist several methods dealing with the distributed optimization problem (9), including distributed descent algorithms, Nedic et al (2010), dual averaging methods, Duchi et al (2012), and the ADMM, Boyd et al (2011);Erseghe et al (2011). However, we make use of the ADMM method, which has become a popular approach for solving convex minimization problems by means of parallelization.…”

Section: We Know That If {α T } H T=1 Contains the D Inverses Of The mentioning

confidence: 99%

“…There exist some works dealing with penalty parameter selection for accelerating the convergence rate of ADMM Ghadimi et al (2012); Boley (2013); Teixeira et al (2013). The convergence analysis is also studied in Boyd et al (2011);Erseghe et al (2011);Boley (2013). In what follows, we describe the derivation of the ADMM algorithm for solving problem (9) with a constant penalty parameter.…”

Section: We Know That If {α T } H T=1 Contains the D Inverses Of The mentioning

confidence: 99%

“…The proposed solution results on solving a convex optimization problem in a distributed way. The Alternating Direction of Multipliers Method (ADMM), that has received a great attention from the community due to its easy implementation, fast convergence, and good accuracy, is adopted to solve the problem, Boyd et al (2011);Erseghe et al (2011).…”

Section: Introductionmentioning

confidence: 99%

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Distributed Estimation of Graph Laplacian Eigenvalues by the Alternating Direction of Multipliers Method

Tran

Kibangou

2014

IFAC Proceedings Volumes

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This paper presents a new method for estimating the eigenvalues of the Laplacian matrix associated with the graph describing the network topology of a multi-agent system. Given an approximate value of the average of the initial condition of the network state and some intermediate values of the network state when performing a Laplacian-based average consensus, the estimation of the Laplacian eigenvalues is obtained by solving the factorization of the averaging matrix. For this purpose, in contrast to the state of the art, we formulate a convex optimization problem that is solved in a distributed way by means of the Alternating Direction Method of Multipliers (ADMM). The main variables in the optimization problem are the coefficients of a polynomial whose roots are precisely the inverse of the distinct nonzero Laplacian eigenvalues. The performance of the proposed method is evaluated by means of simulation results.

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Event‐triggered distributed model predictive control scheme for temperature regulation in multi‐zone air conditioning systems with improved indoor thermal preference indicator

Gao

Zhang

et al. 2023

Adaptive Control & Signal

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Driven by the increasing needs in multi-zone buildings for reducing the air conditioning (A/C) system related energy consumption and increasing the occupants' thermal comfort, an event-triggered distributed model predictive control (DMPC) scheme for building temperature regulation with improved indoor thermal preference indicator is proposed. To this end, a temperature-energy model of the A/C system in a zone which considers multiple types of heat transfer, and the system model of the multi-zone A/C system are derived first. On this basis, an improved indoor thermal preference indicator that trades off the A/C systems related energy consumption with the aggregate thermal comfort of the occupants is proposed for the multi-zone A/C system, then the optimal indoor temperature set-points for each zone are determined by using the distributed consensus algorithm. It is followed by an event-triggered DMPC scheme by adjusting the A/C systems to arrive at the optimal indoor temperature set-points for all the zones with lower communication and computation load. The performance and effectiveness of the proposed methods are demonstrated through a case study on an actual multi-zone A/C system.

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Fast Consensus by the Alternating Direction Multipliers Method

Cited by 139 publications

References 29 publications

The ADMM algorithm for distributed averaging: Convergence rates and optimal parameter selection

The ADMM algorithm for distributed averaging: Convergence rates and optimal parameter selection

Distributed Estimation of Graph Laplacian Eigenvalues by the Alternating Direction of Multipliers Method

Event‐triggered distributed model predictive control scheme for temperature regulation in multi‐zone air conditioning systems with improved indoor thermal preference indicator

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