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    Nonsmooth algorithms and Nesterov’s smoothing technique for generalized Fermat–Torricelli problems

    212818_139705_Nonsmooth_algorithms_-_J._Sun.pdf (316.5Kb)
    Access Status
    Open access
    Authors
    Nam, N.M.
    An, N.T.
    Rector, B.
    Sun, Jie
    Date
    2014
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Nam, N.M. and An, N.T. and Rector, R.B. and Sun, J. 2014. Nonsmooth algorithms and Nesterov’s smoothing technique for generalized Fermat–Torricelli problems. SIAM Journal on Optimization. 24 (4): pp. 1815-1839.
    Source Title
    SIAM Journal on Optimization
    DOI
    10.1137/130945442
    ISSN
    1052-6234
    School
    Department of Mathematics and Statistics
    Remarks

    Copyright © 2014 Society for Industrial and Applied Mathematics. Reproduced with permission

    URI
    http://hdl.handle.net/20.500.11937/2852
    Collection
    • Curtin Research Publications
    Abstract

    We present algorithms for solving a number of new models of facility location which generalize the classical Fermat–Torricelli problem. Our first approach involves using Nesterov’s smoothing technique and the minimization majorization principle to build smooth approximations that are convenient for applying smooth optimization schemes. Another approach uses subgradient-type algorithms to cope directly with the nondifferentiability of the cost functions. Convergence results of the algorithms are proved and numerical tests are presented to show the effectiveness of the proposed algorithms.

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