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?