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

Based on the idea of randomized coordinate descent of α-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a variant of a recent (deterministic) algorithm proposed by Vũ and...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 61; no. 10; pp. 2947 - 2957
Main Authors: Bianchi, Pascal, Hachem, Walid, Iutzeler, Franck
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects:
Consensus algorithms
Convergence
Convex functions
coordinate descent
Cost function
distributed optimization
Mathematics
Minimization
Optimization algorithms
Optimization and Control
primal-dual algorithm
Statistics
Yttrium
Distributed Optimization
Primal-Dual Algorithm
Coordinate Descent
Consensus algorithms
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:Based on the idea of randomized coordinate descent of α-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a variant of a recent (deterministic) algorithm proposed by Vũ and Condat that includes the well-known Alternating Direction Method of Multipliers as a particular case. The obtained algorithm is used to solve asynchronously a distributed optimization problem. A network of agents, each having a separate cost function containing a differentiable term, seek to find a consensus on the minimum of the aggregate objective. The method yields an algorithm where at each iteration, a random subset of agents wake up, update their local estimates, exchange some data with their neighbors, and go idle. Numerical results demonstrate the attractive performance of the method. The general approach can be naturally adapted to other situations where coordinate descent convex optimization algorithms are used with a random choice of the coordinates.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2015.2512043