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Results tagged with convex-analysis
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user 112954
4
votes
Accepted
Regularity of convex sets in $\mathbb{R}^n$
Theorem 1.3 in:
https://arxiv.org/pdf/1304.4179.pdf
and the historical discussion below it is relevant. The result (in a form that applies without the convexity assumption) seems to first appear in 19 …
- 2,772
5
votes
Accepted
For most directions does the supporting hyperplane meeting a bounded convex set meet it in o...
The support function of $C$, restricted to the unit sphere, is differentiable exactly at directions such that (the relevant) hyperplane normal to that direction has a single contact point with $C$.
Be …
- 2,772
8
votes
Accepted
On the convex cone of convex functions
The Laplacian measure of a function in the closure of $G$ is the weak limit of linear combinations of the Laplacian measures of your elementary functions, whose support are "tripods", that is, unions …
- 2,772
5
votes
Accepted
$\arg\max$ in the dual norm of the nuclear norm
The answer is $X^* = uv^*$ where $u$ and $v$ are the left and right singular vectors of $M$ associated with the largest singular value. If the largest singular value has multiplicity larger than $1$, …
- 2,772