How can I use different penalty for different group

[yzhaobk]

In my case, the group size in group lasso in algorithm is not unified and for different group it may should use different penalty (like $\sqrt(p_j)$ where $p_j$ is the degree of freedom of each group).

However, it seems that in your algorithm the penalty coefficients for groups is always the same, which may lead to some inconsistency.

[tomlof]

Assuming you use for instance estimators.LinearRegressionL1L2GL, then you must provide a linear operator for the Nesterov Smoothing. If you generate this operator using functions.nesterov.linear_operator_from_groups, then you can pass a list weights, that contains weights for each individual group. You can see in the doctests for estimators.LinearRegressionL1L2GL how to use it, or in the tests in tests.test_group_lasso.