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A face $ F$ of a convex set $ C$ is a set such that, if $ x \in F$ is a convex combination of other elements in $ C$ , then they must also be in $ F$ . I will denote by $ F(C,x)$ the smallest face of $ C$ which contains $Read more

Let $ \|v\|$ denote some norm in $ \mathbb{R}^n$ . Define a set of matrices as the convex hull of rank-one matrices obtained from vectors in the unit ball of the given norm: $ $ M = \text{hull} \{ v w^T : \|v\|\leq 1, \|w\|\leq 1 \}.$ $ Letting $ S_+$ denote the set ofRead more