Numerische Mathematik

, Volume 141, Issue 2, pp 429–453 | Cite as

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

  • Frédéric de GournayEmail author
  • Jonas Kahn
  • Léo Lebrat


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.

Mathematics Subject Classification

49M15 65D18 46N10 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Frédéric de Gournay
    • 1
    Email author
  • Jonas Kahn
    • 2
  • Léo Lebrat
    • 1
  1. 1.Institut de Mathématiques de Toulouse (UMR 5219), CNRS, INSAUniversité de ToulouseToulouseFrance
  2. 2.Institut de Mathématiques de Toulouse (UMR 5219), CNRS, UPS, IMTUniversité de ToulouseToulouseFrance

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