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

By Xianfeng David Gu, Feng Luo, Jian Sun, Shing-Tung Yau. 2013

146 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/252449b80225599590b35e941cacadeff406e5fa