Volume 40, Number 1, January-March 2006
|Page(s)||1 - 17|
|Published online||01 July 2006|
Numerical solutions of the mass transfer problem
Département de mathématiques et de statistique,
Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal,
H3C 3J7, Canada; firstname.lastname@example.org
2 Department of Mathematics, Columbia Union College, 7600 Flower Avenue, Takoma Park, MD, 20912, USA; email@example.com
Accepted: 7 November 2005
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.
Key words: Continuous programming / transportation / mass transfer / optimization.
© EDP Sciences, 2006
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