Title: Nesterov's Smoothing Technique and Minimizing Differences of Convex Functions for Hierarchical Clustering,
Abstract: 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.