given a convex curve function f(x),
Jensen inequality states:
Preliminary:
Let l(x) be linear function below f(x). Since a convex function is the maximum of all linear functions that lie below it:
>>> this equation I understand.
On the other hand, because f(x) is convex, there is always a value x for which f(x) = l(x), where l(x) is the tangent (or support line) to f(x).
So,
>>> I don't understand at all.
So f(x) = max{l(x)}.
This is a relationship we are going to use to prove Jensen's inequality.
Can anyone explain the problem I have with the 2nd inequality first before I post the rest of the solution (which I can follow.) ?
Thanks.