Geodesic
A D.C. Algorithm via Convex Analysis Approach for Solving a Location Problem Involving Sets
Journal of convex analysis, Tome 23 (2016) no. 1, pp. 77-101
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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.
Classification : 49J52, 49J53, 90C31
Mots-clés : d.c. programming, nonconvex location problem, Pham Dinh - Le Thi algorithm, difference of convex functions, Weiszfeld algorithm 
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     author = {N. T. An and N. M. Nam and N. D. Yen},
     title = {A {D.C.} {Algorithm} via {Convex} {Analysis} {Approach} for {Solving} a {Location} {Problem} {Involving} {Sets}},
     journal = {Journal of convex analysis},
     pages = {77--101},
     year = {2016},
     volume = {23},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2016_23_1_JCA_2016_23_1_a3/}
}
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N. T. An; N. M. Nam; N. D. Yen. A D.C. Algorithm via Convex Analysis Approach for Solving a Location Problem Involving Sets. Journal of convex analysis, Tome 23 (2016) no. 1, pp. 77-101. http://geodesic.mathdoc.fr/item/JCA_2016_23_1_JCA_2016_23_1_a3/