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The group lasso is a penalized regression method, used in regression problemswhere the covariates are partitioned into groups to promote sparsity at thegroup level. Existing methods for finding the group lasso estimator either usegradient projection methods to update the entire coefficient vectorsimultaneously at each step, or update one group of coefficients at a timeusing an inexact line search to approximate the optimal value for the group ofcoefficients when all other groups' coefficients are fixed. We present a newmethod of computation for the group lasso in the linear regression case, theSingle Line Search (SLS) algorithm, which operates by computing the exactoptimal value for each group (when all other coefficients are fixed) with oneunivariate line search. We perform simulations demonstrating that the SLSalgorithm is often more efficient than existing computational methods. We alsoextend the SLS algorithm to the sparse group lasso problem via the SignedSingle Line Search (SSLS) algorithm, and give theoretical results to supportboth algorithms.

Exact block-wise optimization in group lasso and sparse group lasso for linear regression