Nesterov's Smoothing Technique and Minimizing Differences of Convex Functions for Hierarchical Clustering

Autor:	Nam, Nguyen Mau, Geremew, Wondi, Raynolds, Sam, Tran, Tuyen
Rok vydání:	2017
Předmět:	Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	A bilevel hierarchical clustering model is commonly used in designing optimal multicast networks. In this paper, we consider two different formulations of the bilevel hierarchical clustering problem, a discrete optimization problem which can be shown to be NP-hard. Our approach is to reformulate the problem as a continuous optimization problem by making some relaxations on the discreteness conditions. Then Nesterov's smoothing technique and a numerical algorithm for minimizing differences of convex functions called the DCA are applied to cope with the nonsmoothness and nonconvexity of the problem. Numerical examples are provided to illustrate our method.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1701.04464 Zobrazit plný text záznamu View this record from Arxiv