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    Distributed proximal-gradient methods for convex optimization with inequality constraints

    Access Status
    Fulltext not available
    Authors
    Li, J.
    Wu, Changzhi
    Wu, Z.
    Long, Q.
    Wang, Xiangyu
    Date
    2014
    Type
    Journal Article
    
    Metadata
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    Citation
    Li, J. and Wu, C. and Wu, Z. and Long, Q. and Wang, X. 2014. Distributed proximal-gradient methods for convex optimization with inequality constraints. The ANZIAM Journal. 56: pp. 160-178.
    Source Title
    The ANZIAM Journal
    DOI
    10.1017/S1446181114000273
    ISSN
    14468735
    School
    Department of Construction Management
    URI
    http://hdl.handle.net/20.500.11937/41558
    Collection
    • Curtin Research Publications
    Abstract

    We consider a distributed optimization problem over a multi-agent network, in which the sum of several local convex objective functions is minimized subject to global convex inequality constraints. We first transform the constrained optimization problem to an unconstrained one, using the exact penalty function method. Our transformed problem has a smaller number of variables and a simpler structure than the existing distributed primal–dual subgradient methods for constrained distributed optimization problems. Using the special structure of this problem, we then propose a distributed proximal-gradient algorithm over a time-changing connectivity network, and establish a convergence rate depending on the number of iterations, the network topology and the number of agents. Although the transformed problem is nonsmooth by nature, our method can still achieve a convergence rate, O(1/k) , after k iterations, which is faster than the rate, O(1/ sqrt k), of existing distributed subgradient-based methods. Simulation experiments on a distributed state estimation problem illustrate the excellent performance of our proposed method.

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