The relationship between the function and the conjugate

Asked Mar 23 '20 at 13:50

Active Mar 23 '20 at 14:18

Viewed 92 times

Let $f:E\longrightarrow [-\infty,\infty]$ defined by

$$ f^*(y)=max_{x\in {E}}\{<y,x>-f(x)\}$$

is called the conjugate function of $f$. where $y\in{E^*}$ and $E,E^*$ are finite-dimensional real inner product vector spaces with inner product $<.,.>$ and norm $||.||$

Now, I want to know the relationship between the function and the conjugate function.

What is the relationship between the function diagram and the conjugate function diagram?

edited Mar 23 '20 at 14:18

asked Mar 23 '20 at 13:50

SS342

What are $E,E^*, <y,x>$ ? – Mar 23 '20 at 14:10
Maybe you can refer to this problem: Geometric intuition of conjugate function? – Zenan Li Mar 24 '20 at 02:01
thank you very much. – SS342 Mar 25 '20 at 06:42

The relationship between the function and the conjugate

0 Answers0