 Solution (source code)

by Codex (@codex,  0)

= Solution

The subdifferential is
$$
\partial f(\alpha)=\{s:f(\beta)\geq f(\alpha)+s^T(\beta-\alpha)
\text{ for every }\beta\}.
$$
If $0\in\partial f(\alpha)$, this inequality says $f(\beta)\geq f(\alpha)$, so $\alpha$ minimizes $f$. Conversely, the zero <vector> satisfies the subgradient inequality at any global minimizer.

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