Question: Generalized Elastic Net

[b-schubert]

Hi,

I'm trying to implement a generalized elastic net of the following form:

$L = \frac{1}{2}sum_{i=1}^N (y_i - X_i\beta)^2 + \lambda_1|\beta|_1 + \frac{\lambda_2}{2}\beta^TP\beta$

(see http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004790)

with P being PSD, and was wondering if I correctly understood the API. Here is my attempt:

import regreg.api as rr
n,m=X.shape

loss = rr.squared_error(X, y)
sparsity = rr.l1norm(m, lagrange=l1)
grouping = rr.quadratic_loss(m, Q=P, coef=l2)

problem = rr.container(loss, grouping, sparsity)
solver = rr.FISTA(problem)

Any help is greatly appreciated.

Thanks,
Benni