Variational Principles for Minkowski Type Problems, Discrete Optimal Transport, and Discrete Monge-Ampere Equations

Variational Principles for Minkowski Type Problems, Discrete Optimal Transport, and Discrete Monge-Ampere Equations
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DOI：
10.4310/ajm.2016.v20.n2.a7
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发表时间：
2013-02
期刊：
arXiv: Geometric Topology
影响因子：
--
通讯作者：
X. Gu;F. Luo;Jian Sun;S. Yau
X. Gu;F. Luo;Jian Sun;S. Yau
中科院分区：
其他
文献类型：
--
作者：
X. Gu;F. Luo;Jian Sun;S. Yau

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本文对离散最优输运（DOT）、凸多面体的Minkowski型问题和离散Monge-Ampere方程（DMAE）建立了几个相关的有限维变分原理。建立了计算几何中离散最优输运、离散Monge-Ampere方程和功率图之间的联系。
In this paper, we develop several related finite dimensional variational principles for discrete optimal transport (DOT), Minkowski type problems for convex polytopes and discrete Monge-Ampere equation (DMAE). A link between the discrete optimal transport, discrete Monge-Ampere equation and the power diagram in computational geometry is established.