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- W2901450703 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 measure δ 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 ( $G(x,p)=int c(x,y)dp$ ) 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 Γ-convergence theory." @default.
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- W2901450703 date "2018-11-29" @default.
- W2901450703 modified "2023-09-27" @default.
- W2901450703 title "A new class of costs for optimal transport planning" @default.
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- W2901450703 doi "https://doi.org/10.1017/s0956792518000669" @default.
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