Clustering and multifacility location with constraints via distance function penalty methods and dc programming

ABSTRACT

This paper is a continuation of our effort in using mathematical optimization involving DC programming in clustering and multifacility location. We study a penalty method based on distance functions and apply it 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 numerical examples to test our method.

Keywords:

• Clustering
• DC programming
• Nesterov's smoothing techniques
• k-mean algorithm

AMS subject classifications:

• 49J52
• 49J53
• 90C31

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 https://en.wikipedia.org/wiki/List_of_United_States_cities_by_population

2 https://www.mathworks.com/help/map/pcarree.html

Additional information

Funding

Research of Nguyen Mau Nam (Mau Nguyen) was partly supported by the National Science Foundation under grant DMS-1716057. Research of Nguyen Thai An was supported by the Vietnam National Foundation for Science and Technology Development under grant #101.01-2017.325