In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization. There is a lot of literature available, discussing the statistical properties of the regression coefficients estimated by the Lasso method. However, there lacks a comprehensive review discussing the algorithms to solve the optimization problem in Lasso. In this review, we summarize five representative algorithms to optimize the objective function in Lasso, including the iterative shrinkage threshold algorithm (ISTA), fast iterative shrinkage-thresholding algorithms (FISTA), coordinate gradient descent algorithm (CGDA), smooth L1 algorithm (SLA), and path following algorithm (PFA). Additionally, we also compare their convergence rate, as well as their potential strengths and weakness.

翻译：在统计学中，最小绝对收缩与选择算子（Lasso）是一种既能进行变量选择又能实现正则化的回归方法。现有大量文献探讨了Lasso方法所估计回归系数的统计性质，但缺乏系统梳理求解Lasso中优化问题的算法综述。本文总结了五种求解Lasso目标函数的代表性算法，包括迭代收缩阈值算法（ISTA）、快速迭代收缩阈值算法（FISTA）、坐标梯度下降算法（CGDA）、光滑L1算法（SLA）及路径跟踪算法（PFA）。此外，我们还比较了这些算法的收敛速度及其潜在优缺点。