A D.C. Algorithm via Convex Analysis Approach for Solving a Location   Problem Involving Sets
  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. 
Nguyen Thai An, Nguyen Mau Nam, Nguyen Dong Yen
math.OC