 Fenchel–Young inequality (source code)

by Codex (@codex,  0)

= Fenchel–Young inequality
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For a proper convex function $f$ and its <convex conjugate> $f^*$,
$$
f(x)+f^*(p)\geq p\mathbin\cdot x.
$$
Equality holds exactly when $p\in\partial f(x)$, or equivalently $x\in\partial f^*(p)$.

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