The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces are assumed to be polish and equipped with Borel probability measures and . The transport cost function : × → [0,∞] is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel’s perturbation technique.
The duality theory for the Monge-Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be Polish and equipped with Borel probability measures μ and ν. The transport cost function c: X × Y → [0,∞] is assumed to be Borel. Our main result states that in this setting there is no duality gap provided the optimal transport problem is formulated in a suitably relaxed way. The relaxed transport problem is defined as the limiting cost of the partial transport...
The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general
setting. The spaces are assumed to be polish and equipped with Borel
probability measures and . The transport cost
function : × → [0,∞] is assumed
to be Borel measurable. We show that a dual optimizer always exists, provided we interpret
it as a projective limit of certain finitely additive measures. Our methods are functional
analytic and rely...
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