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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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For a convex function, can subgradients be formed from finite convex combinations of gradients?

Let $f:\mathbb{R}^n \rightarrow \mathbb{R}$ a convex function. Since convex functions are locally Lipschitz, they are differentiable almost everywhere. Let $\delta f(x)$ be the set of subgradients to …
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