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Optimal transportation with capacity constraints
Transactions of the American Mathematical Society
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function. Here we consider a natural but largely unexplored variant of this problem by imposing a pointwise constraint on the joint (absolutely continuous) measures: among all joint densities with fixed marginals and which are dominated by a given density, find thedoi:10.1090/s0002-9947-2014-06032-7 fatcat:yyrrqqmwdva6xbvmru2ygwp2l4