Newton-Raphson Consensus for Distributed Convex Optimization

We address the problem of distributed unconstrained convex optimization under separability assumptions, i.e., the framework where each agent of a network is endowed with a local private multidimensional convex cost, is subject to communication constraints, and wants to collaborate to compute the min...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 61; no. 4; pp. 994 - 1009
Main Authors Varagnolo, Damiano, Zanella, Filippo, Cenedese, Angelo, Pillonetto, Gianluigi, Schenato, Luca
Format Journal Article
LanguageEnglish
Published New York IEEE 01.04.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithm design and analysis
Computational geometry
consensus
Control Engineering
Convergence
Convex functions
Convexity
Cost engineering
Cost function
Distributed optimization
Heuristic algorithms
Lyapunov methods
Mathematical models
multi-agent systems
Newton Raphson methods
Optimization
Reglerteknik
smooth functions
Strategy
unconstrained convex optimization
smooth functions
unconstrained convex optimization
multi-agent systems
distributed optimization
Newton-Raphson methods
Consensus
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Summary:We address the problem of distributed unconstrained convex optimization under separability assumptions, i.e., the framework where each agent of a network is endowed with a local private multidimensional convex cost, is subject to communication constraints, and wants to collaborate to compute the minimizer of the sum of the local costs. We propose a design methodology that combines average consensus algorithms and separation of time-scales ideas. This strategy is proved, under suitable hypotheses, to be globally convergent to the true minimizer. Intuitively, the procedure lets the agents distributedly compute and sequentially update an approximated Newton-Raphson direction by means of suitable average consensus ratios. We show with numerical simulations that the speed of convergence of this strategy is comparable with alternative optimization strategies such as the Alternating Direction Method of Multipliers. Finally, we propose some alternative strategies which trade-off communication and computational requirements with convergence speed.
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ISSN:0018-9286
1558-2523
1558-2523
DOI:10.1109/TAC.2015.2449811