Geodesic
Numerical solutions of the mass transfer problem
RAIRO - Operations Research - Recherche Opérationnelle, Tome 40 (2006) no. 1, pp. 1-17

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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.

DOI : 10.1051/ro:2006011
Keywords: continuous programming, transportation, mass transfer, optimization 
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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

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