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math.OC2026
Toland duality and particle approximations for signed Wasserstein barycenters
Thomas Gallouët, Andrea Natale, Gabriele Todeschi
We study the problem of minimizing a weighted sum of squared Wasserstein distances with signed coefficients. In the case of a single positive coefficient, we derive two convex dual…
math.OC2018
Second order models for optimal transport and cubic splines on the Wasserstein space
Jean-David Benamou, Thomas Gallouët, François-Xavier Vialard
On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation. After presenting the natura…