| Date: |
1997 |
| Abstract: |
The classical Fermat-Weber problem is to minimize the sum of the distances from a point in a plane to k given points in the plane. This problem was generalized by Witzgall to n-dimensional space and to allow for a general norm, not necessarily symmetric; he found a dual for this problem. The authors generalize this result further by proving a duality theorem which includes as special cases a great variety of choices of norms in the terms of the Fermat-Weber sum. The theorem is proved by applying a general duality theorem of Rockafellar. As applications, a dual is found for the multi-facility location problem and a nonlinear dual is obtained for a linear programming problem with a priori bounds for the variables. When the norms concerned are continuously differentiable, formulas are obtained for retrieving the solution for each primal problem from the solution of its dual. . |
| Rights: |
Tots els drets reservats.  |
| Language: |
Anglès |
| Document: |
Article ; recerca ; Versió publicada |
| Subject: |
Fermat-Weber problem ;
Facility location ;
Optimization ;
Duality |
| Published in: |
Mathematical Programming, vol. 76 n. 2 (1997) p. 285-297, ISSN 0025-5610 |
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