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Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes

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Can the subdifferential become unbounded at interior points?

Consider $f: \mathbb{R}^n \to \overline{\mathbb{R}}$ a lower-semicontinuous, proper, closed and convex. My question is, can the subdifferential of $\partial f$ be unbounded in the interior of $\text{d …
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