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    Incremental gradient-free method for nonsmooth distributed optimization

    Access Status
    Open access via publisher
    Authors
    Li, J.
    Li, G.
    Wu, Z.
    Wu, Changzhi
    Wang, X.
    Lee, J.
    Jung, K.
    Date
    2017
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Li, J. and Li, G. and Wu, Z. and Wu, C. and Wang, X. and Lee, J. and Jung, K. 2017. Incremental gradient-free method for nonsmooth distributed optimization. Journal of Industrial and management optimization. 13 (4): pp. 1841-1857.
    Source Title
    Journal of Industrial and management optimization
    DOI
    10.3934/jimo.2017021
    ISSN
    1547-5816
    School
    Department of Construction Management
    URI
    http://hdl.handle.net/20.500.11937/57713
    Collection
    • Curtin Research Publications
    Abstract

    In this paper we consider the minimization of the sum of local convex component functions distributed over a multi-agent network. We first extend the Nesterov's random gradient-free method to the incremental setting. Then we propose the incremental gradient-free methods, including a cyclic order and a randomized order in the selection of component function. We provide the convergence and iteration complexity analysis of the proposed methods under some suitable stepsize rules. To illustrate our proposed methods, extensive numerical results on a distributed l 1 -regression problem are presented. Compared with existing incremental subgradient-based methods, our methods only require the evaluation of the function values rather than subgradients, which may be preferred by practical engineers.

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