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.

本研究比较了在求解有约束的 Lasso 问题中的几种不同的计算策略（包括二次规划、交替方向乘子法、以及一种高效的求解路径算法）。在通过模拟和真实数据示例的比较之后，提出了适用于不同数据规模下的实际建议，同时也发现一般化 Lasso 可以转化为有约束的 Lasso 问题，但反之则不成立。因此，该研究的方法也可以用于估计具有广泛应用的一般化 Lasso。