I'm trying to generalise the stacked form of a minimisation problem:
where the L2 norm is often used, so $p=q=2$. This can be brought to
And the left side being equal to the right side would optimise the situation, so taking both the square and the norm out, we are left with a basic matrix equation.
However, if one was to use different norms, that is $p\not=q$, I imagine the solution should change accordingly.
So given the minimisation, for example
how would one start deriving the stacked form?
I tried to search for "optimisation stacked form" and some similar things, but didn't find much. My terminology may be a bit off. Maybe there's a name for this sort of approach?