ABSTRACT 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 benchmark 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 both the Matlab toolbox SparseReg and the Julia package ConstrainedLasso. Supplementary materials for this article are available online.

中文翻译：

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拟合约束套索的算法

摘要 我们比较了解决约束套索问题的替代计算策略。顾名思义，约束套索扩展了广泛使用的套索来处理线性约束，这允许用户将先验信息合并到模型中。除了二次规划之外，我们还采用了乘法器交替方向法（ADMM），并推导出了一种有效的解决路径算法。通过模拟和基准数据示例，我们比较了不同的算法，并针对各种大小的数据的效率和准确性提供了实用的建议。我们还表明，对于任意惩罚矩阵，广义套索可以转换为约束套索，而反之则不然。因此，我们的方法也可用于估计广义套索，其具有广泛的应用。Matlab 工具箱 SparseReg 和 Julia 包 ConstrainedLasso 中均可免费提供用于实现算法的代码。本文的补充材料可在线获取。