Slide 85
Slide 85 text
Literature
The optimal transport problem was first introduced by Monge in 1781
and relaxed by Kantorovich (Nobel prize) in 1940. It defines a distance in
the space of probability distributions, named optimal transport,
Wasserstein distance, or Earth Mover’s distance.
I Mapping/Monge-Amp´
ere equation: Gangbo, Brenier, et.al;
I Gradient flows: Otto, Villani, Ambrosio, Gigli, Savare, Carillo,
Mielke, et.al;
I Hamiltonian flows: Compressible Euler equations, Potential mean
field games, Schrodinger bridge problems, Schrodinger equations:
Benamou, Brenier, Larsy, Lions, Georgiou, Tallenbum, Nelson,
La↵erty, Liu, Gao, et.al.
I Numerical OT and Mean field control/MFG: Benamou, Oberman,
Osher, Achdou, Yang, Justin, Fu, et.al.
I Natural gradient, Mean field control/MFG and Machine learning:
Amari, Li, Chen, Montufar, Yang, Liu, Nurbekyan, Chen, Osher,
Lars, Zhang, Katsoulakis, Zhou, et.al.
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