Can someone suggest me the approach to find the gradient of 4-norm ? eg:(||x||) where it is not a one norm but 4 norm to the power of 4.
I need to solve this question for my practice for the exams. Any input would be helpful. We will consider 4th root for the norm here.
The norm itself must have a 4th root. But in the picture, the function $f$ has a power 4. So we can look at the function simply as $f(x) = x_1^4 + x_2^4 + ... +x_d^4$, where $x_i$s are the components of $x$. Therefore the gradient is simply $$\nabla f = 4 (x_1^3, x_2^3, ..., x_d^3 ) \in \mathbb{R}^d$$