Legendre transformation
= Legendre transformation
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{wiki}
For a function $f$ on a real vector space, its Legendre transformation is the convex conjugate
$$
f^*(p)=\sup_x\{p\mathbin\cdot x-f(x)\}.
$$
When $f$ is differentiable and strictly convex, the maximizing point satisfies $p=\nabla f(x)$.
= Legendre transform
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{synonym}