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Distributed primal-dual stochastic subgradient algorithms for multi-agent optimization under inequality constraints
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DOI：10.1002/rnc.2856.png)
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Abstract
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We consider the multi-agent optimization problem where multiple agents try to cooperatively optimize the sum of their local convex objective functions, subject to global inequality constraints and a convex constraint set over a network. Through characterizing the primal and dual optimal solutions as the saddle points of the associated Lagrangian function, which can be evaluated with stochastic errors, we propose the distributed primal-dual stochastic subgradient algorithms for two cases: (i) the time model is synchronous and (ii) the time model is asynchronous. In the first case, we obtain bounds on the convergence properties of the algorithm for a diminishing step size. In the second case, for a constant step size, we establish some error bounds on the algorithm's performance. In particular, we prove that the error bounds scale as n root n in the number of n agents. Copyright (c) 2012 John Wiley & Sons, Ltd.
Keywords:
multi-agent systems
convex optimization
subgradient methods
distributed average consensus
gossip algorithms
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