  We compare alternative computing strategies for solving the constrained lasso
problem. As its name suggests, the constrained lasso extends the widely-used
lasso to handle linear constraints, which allow the user to incorporate prior
information into the model. In addition to quadratic programming, we employ the
alternating direction method of multipliers (ADMM) and also derive an efficient
solution path algorithm. Through both simulations and real data examples, we
compare the different algorithms and provide practical recommendations in terms
of efficiency and accuracy for various sizes of data. We also show that, for an
arbitrary penalty matrix, the generalized lasso can be transformed to a
constrained lasso, while the converse is not true. Thus, our methods can also
be used for estimating a generalized lasso, which has wide-ranging
applications. Code for implementing the algorithms is freely available in the
Matlab toolbox SparseReg.
