Group Lasso
= Group Lasso
{c}
{wiki}
The group Lasso partitions a coefficient vector into groups $G_1,\ldots,G_q$ and replaces the coordinatewise $\ell^1$ penalty with a weighted sum of group norms,
$$
P(\beta)=\sum_{j=1}^q m_j\lVert\beta_{G_j}\rVert_2.
$$
It tends to retain or discard an entire group at once. Its dual norm is
$$
P^*(v)=\max_j m_j^{-1}\lVert v_{G_j}\rVert_2,
$$
so the corresponding <Holder inequality> is $|u^Tv|\leq P(u)P^*(v)$.