Definition 3.31 . [02LA]

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Definition 3.31.

Let $f$ be a closed concave function. The Legendre-Fenchel correspondence of $f$ is defined as

{\mathcal{L}}f\colon\Pi(f)\longrightarrow\Pi(f^{\vee}),\quad C\longmapsto\bigcap_{u\in C}\partial f(u).