Geodesic
A Framework for Wasserstein-1-Type Metrics
Journal of convex analysis, Tome 26 (2019) no. 2, pp. 353-396
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We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy measure between nonnegative measures of different mass. This generalization inherits the convexity and computational efficiency from the Wasserstein-1 metric, and it includes several previous approaches from the literature as special cases. For various specific instances of the generalized Wasserstein-1 metric we furthermore demonstrate their usefulness in applications by numerical experiments.
Classification : 49M29, 65K10
Mots-clés : Convex optimization, unbalanced optimal transport, minimum-cost flow, Kantorovich-Rubinstein formula 
@article{JCA_2019_26_2_JCA_2019_26_2_a0,
     author = {B. Schmitzer and B. Wirth},
     title = {A {Framework} for {Wasserstein-1-Type} {Metrics}},
     journal = {Journal of convex analysis},
     pages = {353--396},
     year = {2019},
     volume = {26},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2019_26_2_JCA_2019_26_2_a0/}
}
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B. Schmitzer; B. Wirth. A Framework for Wasserstein-1-Type Metrics. Journal of convex analysis, Tome 26 (2019) no. 2, pp. 353-396. http://geodesic.mathdoc.fr/item/JCA_2019_26_2_JCA_2019_26_2_a0/