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.
