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

Nguyen Mau Nam (), R. Blake Rector () and Daniel Giles ()
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Nguyen Mau Nam: Portland State University
R. Blake Rector: Portland State University
Daniel Giles: Portland State University

Journal of Optimization Theory and Applications, 2017, vol. 173, issue 1, No 12, 255-278

Abstract: 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.

Keywords: Difference of convex functions; Nesterov smoothing technique; Fermat–Torricelli problem; Multifacility location; Clustering; 49J52; 49J53; 90C31 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-017-1075-6

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