Fenchel–Moreau theorem

In convex analysis, the Fenchel–Moreau theorem (named after Werner Fenchel and Jean Jacques Moreau) or Fenchel biconjugation theorem (or just biconjugation theorem) is a theorem which gives necessary and sufficient conditions for a function to be equal to its biconjugate. This is in contrast to the general property that for any function ${\displaystyle f^{**}\leq f}$. This can be seen as a generalization of the bipolar theorem. It is used in duality theory to prove strong duality (via the perturbation function).