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Numerical solutions of the mass transfer problem
Published online by Cambridge University Press: 01 July 2006
Abstract
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.
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- © EDP Sciences, 2006
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