  We develop fast and scalable algorithms based on block-coordinate descent to
solve the group lasso and the group elastic net for generalized linear models
along a regularization path. Special attention is given when the loss is the
usual least squares loss (Gaussian loss). We show that each block-coordinate
update can be solved efficiently using Newton's method and further improved
using an adaptive bisection method, solving these updates with a quadratic
convergence rate. Our benchmarks show that our package adelie performs 3 to 10
times faster than the next fastest package on a wide array of both simulated
and real datasets. Moreover, we demonstrate that our package is a competitive
lasso solver as well, matching the performance of the popular lasso package
glmnet.
