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OLS regression minimizes the sum of the squared errors. The normal equation for an OLS for $L_2$ minimization is as follows: $$b= (A'A)^{-1}A'y$$

What would be the equation to minimize the $L_4$ norm for an overdetermined system. How would I derive generalizations for any arbitrary even norm such as $L_6$, $L_8$ and so on. This question is related to:

Why least squares?

Not very familiar with matrix calculus so a gentle introduction would be much appreciated. Thanks.

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I don't know that much, but there might not be any closed-form solution. $L_2$ is easy because it has a simple derivative. – Simon Kuang Jun 1 at 19:58

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