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Journal of Convex Analysis 23 (2016), No. 1, 077--101
Copyright Heldermann Verlag 2016

A D.C. Algorithm via Convex Analysis Approach for Solving a Location Problem Involving Sets

Nguyen Thai An
Thua Thien Hue College of Education, 123 Nguyen Hue, Hue City, Vietnam

Nguyen Mau Nam
Fariborz Maseeh Dept. of Mathematics and Statistics, Portland State University, PO Box 751, Portland, OR 97207, U.S.A.

Nguyen Dong Yen
Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi 10307, Vietnam

We study a location problem that involves a weighted sum of distances to closed convex sets. As several of the weights might be negative, traditional solution methods of convex optimization are not applicable. After obtaining some existence theorems, we introduce a simple, but effective, algorithm for solving the problem. Our method is based on the Pham Dinh - Le Thi algorithm for d.c. programming and a generalized version of the Weiszfeld algorithm, which works well for convex location problems.

Keywords: d.c. programming, nonconvex location problem, Pham Dinh - Le Thi algorithm, difference of convex functions, Weiszfeld algorithm.

MSC: 49J52, 49J53, 90C31

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