Legendre Transform and Lagrange Dual
* Both of them are defined in convex functions
* Both of them can be generalized to non-convex function but extended to convex hull
* Legendre transform is more general and (sort of) unique f(x) -> f*(v) -> f(x). f*(v) is conjugate function.
* Lagrange dual is only for minimum value equivalent; depending on the constraints, Lagrange dual can be more than one.
* Lagrange dual can utilize conjugate function.
Fenchel duality theorem