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

Xianfeng Gu; Feng Luo; Jian Sun; S. -T. Yau

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arXiv · 1302.5472

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

Xianfeng Gu·Feng Luo·Jian Sun·S. -T. Yau

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Abstract

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.

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Xianfeng Gu, Feng Luo, Jian Sun, S. -T. Yau. 2013-02-22. Variational Principles for Minkowski Type Problems, Discrete Optimal Transport, and Discrete Monge-Ampere Equations. https://arxiv.org/abs/1302.5472

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