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Differentiation and regularity of semi-discrete optimal transport with respect to the parameters of the discrete measure


This paper aims at determining under which conditions the semi-discrete optimal transport is twice differentiable with respect to the parameters of the discrete measure and exhibits numerical applications. The discussion focuses on minimal conditions on the background measure to ensure differentiability. We provide numerical illustrations in stippling and blue noise problems.

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Correspondence to Frédéric de Gournay.

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de Gournay, F., Kahn, J. & Lebrat, L. Differentiation and regularity of semi-discrete optimal transport with respect to the parameters of the discrete measure. Numer. Math. 141, 429–453 (2019).

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