Convex analysis is the study of properties of convex sets and convex functions. For questions about optimization of convex functions over convex sets, please use the (convex-optimization) tag.

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interior of convex hull relatively open

Consider $k+1$ affinely independent vectors $\left\{p_0,p_1, \dots, p_k \right \}$ in $n$-dimensional euclidean vector space $n>k$ and consider their convex hull. It is known that each point $x$ of ...
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Why is the Barycenter operation in Hadamard spaces Lipschitz continuous?

I am looking into exercise 9.2.22 of "A course in metric geometry" by Burago-Burago-Ivanov. For a Hadamard space $H$ (a complete simply connected metric space of nonpositive curvature in the ...