Biconjugation as closed convexification
= Biconjugation as closed convexification
{title2=$f^{**}=\operatorname{cl\,conv}f$}
For a proper extended-real <function> with an <affine minorant>, <biconjugate> gives its greatest lower-semicontinuous <convex> minorant. Geometric separation of its <epigraph> turns containing <closed half-spaces> into affine lower bounds. Vertical half-spaces are recovered by adding multiples of a domain-separating inequality to one fixed affine minorant.