Journal of Convex Analysis 26 (2019), No. 2, 353--396
Copyright Heldermann Verlag 2019
A Framework for Wasserstein-1-Type Metrics
Bernhard Schmitzer
Institut für Analysis und Numerik, Westfälische Wilhelms-Universität, Einsteinstr. 62, 48149 Münster, Germany
schmitzer@uni-muenster.de
Benedikt Wirth
Institut für Analysis und Numerik, Westfälische Wilhelms-Universität, Einsteinstr. 62, 48149 Münster, Germany
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.
Keywords: Convex optimization, unbalanced optimal transport, minimum-cost flow, Kantorovich-Rubinstein formula.
MSC: 49M29, 65K10
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