Theorem 13.2.7 (Dual Representation for Closed Convex Sets).label Let $C\suf\R^{n}$ be a nonempty closed convex set then
\begin{align*}C=\caps{}{y\in\R^n}\curl{x\in\R^n:\inner{x}{y}\leq h_C(y)}\end{align*}
where $h_{C}(y)=\infty$ imposes no restriction.
Proof. check notes$\square$
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