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

被引：14
|
作者：
de Gournay, Frederic [1 ]
Kahn, Jonas [2 ]
Lebrat, Leo [1 ]
机构：
[1] Univ Toulouse, CNRS, Inst Math Toulouse, INSA,UMR 5219, F-31077 Toulouse, France
[2] Univ Toulouse, CNRS, Inst Math Toulouse, UPS,IMT,UMR 5219, F-31062 Toulouse, France
来源：
NUMERISCHE MATHEMATIK | 2019年 / 141卷 / 02期
关键词：
ALGORITHM; QUANTIZATION;
D O I：
10.1007/s00211-018-1000-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：429 / 453
页数：25
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