Suppose $\displaystyle f(\vec{x})=\max_ix_i$. What is the gradient $\displaystyle \bigtriangledown f(\vec{x})=?$

Any help appreciated.

Printable View

- Oct 8th 2009, 12:10 AMnoschemerGradient for the max function
Suppose $\displaystyle f(\vec{x})=\max_ix_i$. What is the gradient $\displaystyle \bigtriangledown f(\vec{x})=?$

Any help appreciated. - Oct 8th 2009, 04:15 AMHallsofIvy
I don't believe that is a differentiable function.

- Oct 8th 2009, 10:48 PMnoschemer
THanks for ur reply. Can u provide a brief explanation for the non-differentiability of this function?? My major is electrical engineering, and background in analysis is not good.

- Oct 9th 2009, 06:21 AMHallsofIvy
If you were to graph max(x,y) on, say $\displaystyle -1\le x\le 1$, $\displaystyle -1\le y\le 1$ you would see sharp corners along the lines y= x and y= -x. Generally speaking, only "smooth" functions have derivatives.