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Let and be two probability measures on the real line and
let be a lower semicontinuous function on the plane. The mass
transfer problem consists in determining a measure whose
marginals coincide with and , and whose total cost
d 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 . We illustrate these
numerical methods and determine the convergence...
Let and be two compact spaces endowed with
respective measures and satisfying the condition . Let be a continuous function on the product space . The mass transfer problem consists in determining a measure on
whose marginals coincide with and , and such that
the total cost be minimized. We first
show that if the cost function is decomposable, i.e., can be
represented as the sum of two continuous functions defined on and
, respectively, then every feasible measure is optimal. Conversely,
when...
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