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Search: All articles in the CJM digital archive with keyword marginal

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1. CJM Online first

Yin, Jiang
Absolute continuity of Wasserstein barycenters over Alexandrov spaces
In this paper, we prove that, on a compact, $n$-dimensional Alexandrov space with curvature $\geqslant -1$, the Wasserstein barycenter of Borel probability measures $\mu_1,...,\mu_m$ is absolutely continuous with respect to the $n$-dimensional Hausdorff measure if one of them is.

Keywords:Alexandrov space, Wasserstein barycenter, multi-marginal optimal transport
Categories:51K05, 49K30

2. CJM 2004 (vol 56 pp. 825)

Penot, Jean-Paul
Differentiability Properties of Optimal Value Functions
Differentiability properties of optimal value functions associated with perturbed optimization problems require strong assumptions. We consider such a set of assumptions which does not use compactness hypothesis but which involves a kind of coherence property. Moreover, a strict differentiability property is obtained by using techniques of Ekeland and Lebourg and a result of Preiss. Such a strengthening is required in order to obtain genericity results.

Keywords:differentiability, generic, marginal, performance function, subdifferential
Categories:26B05, 65K10, 54C60, 90C26, 90C48

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