Abstract
We extend our work on the optimal mapping of distributions in three directions: (a) we consider any set-valued mapping, not just diffeomorphisms; (b) we distinguish between weak and strong optimality, and identify strong optimality with cyclic monotonicity; and (c) we prove that, under some restrictions, a weakly optimal mapping has the subgradient property.
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Communicated by D. Q. Mayne
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Smith, C.S., Knott, M. Note on the optimal transportation of distributions. J Optim Theory Appl 52, 323–329 (1987). https://doi.org/10.1007/BF00941290
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DOI: https://doi.org/10.1007/BF00941290