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Strong convexity inequality w.r.t. infinity norm $\lVert\cdot\rVert_{\infty}$

I think it is not possible to do much better than $\frac{1}{\sqrt n}$. More precisely, I believe the best $\alpha$ is $\frac{1}{\sqrt n}$ whenever $n$ is a power of $2$, and therefore (since $\alpha$ …
Mikael de la Salle's user avatar