1. Minimizing Differences of Convex Functions with Applications to Facility Location and Clustering
- Author
-
Nguyen Mau Nam, Daniel Giles, and R. Blake Rector
- Subjects
Convex hull ,Convex analysis ,Mathematical optimization ,021103 operations research ,Control and Optimization ,Applied Mathematics ,Random coordinate descent ,010102 general mathematics ,0211 other engineering and technologies ,Proper convex function ,02 engineering and technology ,Subderivative ,Management Science and Operations Research ,01 natural sciences ,Convex optimization ,Convex combination ,0101 mathematics ,Conic optimization ,Mathematics - 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.
- Published
- 2017