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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

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Is an ambiguity set with Wasserstein distance of order 1 is convex?

I have a question about the convexity of an Wasserstein ambiguity set. Let $W_1(\mu, \nu)$ be the Wasserstein distance of order 1 between $\mu$ and $\nu$, defined as $$W_1(\mu, \nu) := \min\limits_{ …
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