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?

  • 1
    $\begingroup$ I doubt this is possible for $p\ne q$. $\endgroup$ – daw Nov 22 '18 at 20:34
  • $\begingroup$ If you think the minimum will be 0 then you can always write the system of equations $Ax=y$ and $Dx=0$. But in practice one uses regression for very overdetermined systems. $\endgroup$ – Michal Adamaszek Nov 23 '18 at 7:40

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