Accepted Paper
Inserted: 1 oct 2012
Last Updated: 5 jan 2013
Journal: Set-Valued and Variational Analysis
Year: 2013
Abstract:
The main result of this paper is the existence of an optimal transport map $T$ between two given measures $\mu$ and $\nu$, for a cost which considers the maximal oscillation of $T$ at scale $\delta$, given by $\omega_\delta(T):=\sup_{\vert x-y\vert<\delta}\vert T(x)-T(y) \vert$. The minimization of this criterion finds applications in the field of privacy-respectful data transmission. The existence proof unfortunately only works in dimension one and is based on some monotonicity considerations.
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