[Optimization] Convex Functions
3. The conjugate function
Definition and examples
Let $f : R^n \rightarrow R$. The conjugate of the function f, $f* : R^n \rightarrow R$,
\[f*(y) = sup_{x \in \textbf{dom} f}(y^Tx - f(x))\]$f*$ is a convex function whether or not $f$ is convex
Reference
Stephen Boyd - Convex Optimization