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Home > Articles > Published articles > Duality theorem for a generalized FermatWeber problem 
Date:  1997 
Abstract:  The classical FermatWeber 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 ndimensional 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 FermatWeber sum. The theorem is proved by applying a general duality theorem of Rockafellar. As applications, a dual is found for the multifacility 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. . 
Language:  Anglès. 
Document:  Article ; recerca ; article ; publishedVersion 
Subject:  FermatWeber problem ; Facility location ; Optimization ; Duality 
Published in:  Mathematical Programming, vol. 76 n. 2 (1997) p. 285297, ISSN 00255610 
13 p, 616.7 KB UAB restricted access 
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