Numerical solutions of the mass transfer problem
RAIRO - Operations Research - Recherche Opérationnelle, Tome 40 (2006) no. 1, p. 1-17
Let μ and ν be two probability measures on the real line and let c be a lower semicontinuous function on the plane. The mass transfer problem consists in determining a measure ξ whose marginals coincide with μ and ν, and whose total cost c(x,y)dξ(x,y) is minimum. In this paper we present three algorithms to solve numerically this Monge-Kantorovitch problem when the commodity being shipped is one-dimensional and not necessarily confined to a bounded interval. We illustrate these numerical methods and determine the convergence rate.
@article{RO_2006__40_1_1_0,
     author = {Dubuc, Serge and Kagabo, Issa},
     title = {Numerical solutions of the mass transfer problem},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {1},
     year = {2006},
     pages = {1-17},
     doi = {10.1051/ro:2006011},
     zbl = {pre05140663},
     mrnumber = {2248419},
     language = {en},
     url = {http://www.numdam.org/item/RO_2006__40_1_1_0}
}
Dubuc, Serge; Kagabo, Issa. Numerical solutions of the mass transfer problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 40 (2006) no. 1, pp. 1-17. doi : 10.1051/ro:2006011. http://www.numdam.org/item/RO_2006__40_1_1_0/

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