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Trivial Cases for the Kantorovitch Problem

Serge DubucIssa KagaboPatrice Marcotte — 2010

RAIRO - Operations Research

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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