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Title of Journal: J Optim Theory Appl

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Abbravation: Journal of Optimization Theory and Applications

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Springer US

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DOI

10.1007/bf01091314

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1573-2878

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Distributed Stochastic Subgradient Projection Algo

Authors: S Sundhar Ram A Nedić V V Veeravalli
Publish Date: 2010/07/22
Volume: 147, Issue: 3, Pages: 516-545
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Abstract

We consider a distributed multiagent network system where the goal is to minimize a sum of convex objective functions of the agents subject to a common convex constraint set Each agent maintains an iterate sequence and communicates the iterates to its neighbors Then each agent combines weighted averages of the received iterates with its own iterate and adjusts the iterate by using subgradient information known with stochastic errors of its own function and by projecting onto the constraint setThe goal of this paper is to explore the effects of stochastic subgradient errors on the convergence of the algorithm We first consider the behavior of the algorithm in mean and then the convergence with probability 1 and in mean square We consider general stochastic errors that have uniformly bounded second moments and obtain bounds on the limiting performance of the algorithm in mean for diminishing and nondiminishing stepsizes When the means of the errors diminish we prove that there is mean consensus between the agents and mean convergence to the optimum function value for diminishing stepsizes When the mean errors diminish sufficiently fast we strengthen the results to consensus and convergence of the iterates to an optimal solution with probability 1 and in mean square

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