Grouped Lasso

${\hat{\beta }}_{\text{grouped lasso}}=\underset{\beta }{\mathrm{argmin}}(\mathbf{y}-\mathbf{X}\beta {)}^{⊺}(\mathbf{y}-\mathbf{X}\beta )+\lambda \sum _{l=1}^L\sqrt{p_l}||{\beta }_l|{|}_2$ where $L$ is the number of groups, $p_l$ is the number of variables within the group $l$, and $||\cdot |{|}_2$ is Euclidean Norm

In grouped lasso, the variables in each group share a regularization parameter.