# How is the generalization of LASSO called?

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?