Minimizing Differences of Convex Functions with Applications to Facility Location and Clustering
Minimizing Differences of Convex Functions with Applications to Facility Location and Clustering
复制标题
最小化凸函数的差异及其在设施定位和聚类中的应用
DOI：
--
复制
发表时间：
2017
影响因子：
1.9
通讯作者：
Daniel Giles
中科院分区：
文献类型：
--
作者：
N. M. Nam;R. Rector;Daniel Giles
在本文中，我们开发的算法来解决广义费马-托里切利问题的正负权重和多设施的位置问题，涉及的距离产生的闵可夫斯基规范。我们还介绍了一种新的聚类模型的基础上平方距离凸集。利用Nesterov光滑技术和由Tao和An引入的凸函数的最小化差的算法，我们开发了解决这些问题的有效算法。我们证明了各种数值例子的算法。
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.