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Minimizing Differences of Convex Functions with Applications to Facility Location and Clustering

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  • Nguyen Mau Nam

    (Portland State University)

  • R. Blake Rector

    (Portland State University)

  • Daniel Giles

    (Portland State University)

Abstract

In this paper, we develop algorithms to solve generalized Fermat–Torricelli problems with both positive and negative weights and multifacility location problems involving distances generated by Minkowski gauges. We also introduce a new model of clustering based on squared distances to convex sets. Using the Nesterov smoothing technique and an algorithm for minimizing differences of convex functions introduced by Tao and An, we develop effective algorithms for solving these problems. We demonstrate the algorithms with a variety of numerical examples.

Suggested Citation

  • Nguyen Mau Nam & R. Blake Rector & Daniel Giles, 2017. "Minimizing Differences of Convex Functions with Applications to Facility Location and Clustering," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 255-278, April.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:1:d:10.1007_s10957-017-1075-6
    DOI: 10.1007/s10957-017-1075-6
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    References listed on IDEAS

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    1. Zvi Drezner, 2009. "On the convergence of the generalized Weiszfeld algorithm," Annals of Operations Research, Springer, vol. 167(1), pages 327-336, March.
    2. Thomas Jahn & Yaakov S. Kupitz & Horst Martini & Christian Richter, 2015. "Minsum Location Extended to Gauges and to Convex Sets," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 711-746, September.
    3. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. W. Geremew & N. M. Nam & A. Semenov & V. Boginski & E. Pasiliao, 2018. "A DC programming approach for solving multicast network design problems via the Nesterov smoothing technique," Journal of Global Optimization, Springer, vol. 72(4), pages 705-729, December.
    2. Nguyen Thai An & Nguyen Mau Nam & Xiaolong Qin, 2020. "Solving k-center problems involving sets based on optimization techniques," Journal of Global Optimization, Springer, vol. 76(1), pages 189-209, January.

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