A Distributed Algorithm for Convex Constrained Optimization Under Noise

We present a novel distributed algorithm for convex constrained optimization problems that are subject to noise corruption and uncertainties. The proposed scheme can be classified as a distributed stochastic approximation method, where a unique feature here is that we allow for multiple noise terms...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 61; no. 9; pp. 2496 - 2511
Main Authors: Chatzipanagiotis, Nikolaos, Zavlanos, Michael M.
Format: Journal Article
Language:English
Published: New York IEEE 01.09.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation
Approximation algorithms
Approximation methods
Constraints
Convergence
Distributed algorithms
Distributed optimization
Economic models
Lagrange multiplier
Linear programming
Mathematical analysis
Mathematical models
multi-agent systems
Noise
noisy communications
Optimization
stochastic approximation
stochastic optimization
Stochasticity
Uncertainty
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:We present a novel distributed algorithm for convex constrained optimization problems that are subject to noise corruption and uncertainties. The proposed scheme can be classified as a distributed stochastic approximation method, where a unique feature here is that we allow for multiple noise terms to appear in both the computation and communication stages of the distributed iterative process. Specifically, we consider problems that involve multiple agents optimizing a separable convex objective function subject to convex local constraints and linear coupling constraints. This is a richer class of problems compared to those that can be handled by existing distributed stochastic approximation methods which consider only consensus constraints and fewer sources of noise. The proposed algorithm utilizes the augmented Lagrangian (AL) framework, which has been widely used recently to solve deterministic optimization problems in a distributed way. We show that the proposed method generates sequences of primal and dual variables that converge to their respective optimal sets almost surely.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2015.2504932