A note on the uniqueness of solutions to the transportation problem

Citation
S. Dubuc et al., A note on the uniqueness of solutions to the transportation problem, INFOR, 37(2), 1999, pp. 141-148
Citations number
9
Categorie Soggetti
Engineering Mathematics
Journal title
INFOR
ISSN journal
03155986 → ACNP
Volume
37
Issue
2
Year of publication
1999
Pages
141 - 148
Database
ISI
SICI code
0315-5986(199905)37:2<141:ANOTUO>2.0.ZU;2-R
Abstract
Let mu and nu be two probability measures on the real line and c be a lower semicontinuous function on the plane. The mass transfer problem consists i n determining a measure xi with respective marginals mu and nu that minimiz es the functional integral cd xi. In this paper we show that, whenever the function c is strictly superadditive, the solution corresponding to the low er Frechet bound is the unique optimal solution. This result also holds for the discrete version of the problem.