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A new class of cost for optimal transport planning

Abstract : We study a class of optimal transport planning problems where the reference cost involves a non linear function G(x, p) representing the transport cost between the Dirac mesure x and a target probability p. This allows to consider interesting models which favour multi-valued transport maps in contrast with the classical linear case (G(x, p) = R c(x, y) dp) where finding single-valued optimal transport is a key issue. We present an existence result and a general duality principle which apply to many examples. Moreover, under a suitable subadditivity condition, we derive a Kantorovich-Rubinstein version of the dual problem allowing to show existence in some regular cases. We also consider the well studied case of Martingale transport and present some new perspectives for the existence of dual solutions in connection with-convergence theory.
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https://hal-univ-tln.archives-ouvertes.fr/hal-03353658
Contributor : Guy Bouchitte Connect in order to contact the contributor
Submitted on : Friday, September 24, 2021 - 11:24:26 AM
Last modification on : Saturday, September 25, 2021 - 3:14:02 AM

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Jean-Jacques Alibert, Guy Bouchitté, Thierry Champion. A new class of cost for optimal transport planning. European Journal of Applied Mathematics, Cambridge University Press (CUP), 2019, 30 (6), pp.1229-1263. ⟨10.1017/s0956792518000669⟩. ⟨hal-03353658⟩

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