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math.AP2012★ 1 cited
On the degeneracy of optimal transportation
Young-Heon Kim, Jun Kitagawa
We extend a dimensional upper bound on how much an optimal transport map can degenerate for the quadratic transportation cost, originally due to Caffarelli, to cost functions that…
math.OC2012★ 2 cited
An iterative scheme for solving the optimal transportation problem
Jun Kitagawa
We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Addition…