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

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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.

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Notes

  1. Available at https://archive.ics.uci.edu/ml/datasets.html.

  2. http://www.realestate3d.com/gps/uslatlongdegmin.htm.

  3. Available at https://en.wikipedia.org/wiki/List_of_United_States_cities_by_population.

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Acknowledgements

The research of Nguyen Mau Nam was partially supported by the US National Science Foundation under Grant DMS-1411817.

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Authors and Affiliations

  1. Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, PO Box 751, Portland, OR, 97207, USA

    Nguyen Mau Nam, R. Blake Rector & Daniel Giles

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  1. Nguyen Mau Nam
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  2. R. Blake Rector
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  3. Daniel Giles
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Correspondence to Nguyen Mau Nam.

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Communicated by Horst Martini.

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Nam, N.M., Rector, R.B. & Giles, D. Minimizing Differences of Convex Functions with Applications to Facility Location and Clustering. J Optim Theory Appl 173, 255–278 (2017). https://doi.org/10.1007/s10957-017-1075-6

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  • DOI: https://doi.org/10.1007/s10957-017-1075-6

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