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I know that ridge regression is a special case of Tykhonv regularization. In fact with Tykhonov one tries to minimize:

$|| Ax - b ||^2 +|| \Gamma x ||^2$

If $\Gamma$ is the identity matrix scaled by a coefficient we have ridge regression(Is Tikhonov regularization the same as Ridge Regression?).

In LASSO regression one seeks to minimize:

$|| Ax - b ||^2 +\lambda || x ||^1$

How would be called a more general case with the form:

$|| Ax - b ||^2 + || \Gamma x ||^1$

What would be useful for?

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