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Consider the space of probability densities $(P(\mathbb{R}^d), W_2)$ (probability measures on $\mathbb{R}^d$ with 2-Wasserstein distance). How can we determine if a subset $Q$ is convex? I know that a ...

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_{\...