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

Frédéric de Gournay (1) , Jonas Kahn (2) , Léo Lebrat

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LPP - Laboratoire Paul Painlevé - UMR 8524

This paper aims at determining under which conditions the semi-discrete optimal transport is twice dierentiable 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 dierentiability. We provide numerical illustrations in stippling and blue noise problems.

Domaines: Analyse numérique [math.NA]

Frédéric de Gournay, Jonas Kahn, Léo Lebrat. Differentiation and regularity of semi-discrete optimal transport with respect to the parameters of the discrete measure. 2018. ⟨hal-01721681v1⟩