 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-4/30k/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

\partial f (α) = {s : f (β) \geq f (α) + s^{T} (β - α) for every β} .

0 \in \partial f (α)

, this inequality says

f (β) \geq f (α)

, so

α

minimizes

f

. Conversely, the zero vector satisfies the subgradient inequality at any global minimizer.

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