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Overview
The optimal transport has many different formulations under various
angles:
Mapping/Monge-Amp´
ere equation ;
Linear programming ;
Geometry/Fluid dynamics/L1 minimization ;
which are considered by Otto, Kinderlehrer, Villani, McCann, Carlen,
Lott, Strum, Gangbo, Jordan, Evans, Brenier, Benamou, Ambrosio, Gigli,
Savare and many more.
In this talk, we mainly follow its geometric formulation in a discrete
setting.
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