Fenchel's duality theorem

In mathematics, Fenchel's duality theorem is a result in the theory of convex functions named after Werner Fenchel. Let f {\displaystyle f} be a proper convex function on R n {\displaystyle \mathbb {R} ^{n}} and let g {\displaystyle g} be a proper concave function on R n {\displaystyle \mathbb {R} ^{n}} .