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Constrained Clustering and Multifacility Location via Distance Function Penalty Method and DC Programming

Nguyen Mau Nam(mnn3***at***pdx.edu)
Wondi Geremew(geremeww***at***stockton.edu)
Sam Reynolds(ser6***at***pdx.edu)
Tuyen Tran(tuyen2***at***pdx.edu)

Abstract: Cluster analysis tackles an emerging class of optimization problems that have numerous applications in data science, machine learning, and multifacility location problems, to name a few. This paper is a continuation of our effort in using mathematical optimization in clustering. We study a penalty method based on distance functions and apply particularly to a number of problems in clustering and multifacility location in which the centers to be found must lie in some given set constraints. We also provide different numerical examples to test our method.

Keywords: Clustering, DC programming, Nesterov's smoothing technique, k-mean algorithm

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation:

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Entry Submitted: 08/04/2017
Entry Accepted: 08/04/2017
Entry Last Modified: 08/04/2017

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