Minimizing Differences of Convex Functions with Applications to Facility Location and Clustering
Convex functions, Algorithms, Optimization (Mathematics)
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 called the DCA introduced by Tao and An, we develop effective algorithms for solving these problems. We demonstrate the algorithms with a variety of numerical examples.
Nguyen, Mau Nam; Rector, R. Blake; and Giles, Daniel J., "Minimizing Differences of Convex Functions with Applications to Facility Location and Clustering" (2016). Mathematics and Statistics Faculty Publications and Presentations. 165.
This is the author’s version of a work that was accepted for publication in Journal of Optimization Theory and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Optimization Theory and Applications, 2017 DOI: 10.1007/s10957-017-1075-6. The article is available online at: https://doi.org/10.1007/s10957-017-1075-6