  Variable selection is one of the most important tasks in statistics and
machine learning. To incorporate more prior information about the regression
coefficients, the constrained Lasso model has been proposed in the literature.
In this paper, we present an inexact augmented Lagrangian method to solve the
Lasso problem with linear equality constraints. By fully exploiting
second-order sparsity of the problem, we are able to greatly reduce the
computational cost and obtain highly efficient implementations. Furthermore,
numerical results on both synthetic data and real data show that our algorithm
is superior to existing first-order methods in terms of both running time and
solution accuracy.
