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In statistics, the least absolute shrinkage and selection operator (Lasso) isa regression method that performs both variable selection and regularization.There is a lot of literature available, discussing the statistical propertiesof the regression coefficients estimated by the Lasso method. However, therelacks a comprehensive review discussing the algorithms to solve theoptimization problem in Lasso. In this review, we summarize five representativealgorithms to optimize the objective function in Lasso, including the iterativeshrinkage threshold algorithm (ISTA), fast iterative shrinkage-thresholdingalgorithms (FISTA), coordinate gradient descent algorithm (CGDA), smooth L1algorithm (SLA), and path following algorithm (PFA). Additionally, we alsocompare their convergence rate, as well as their potential strengths andweakness.

A Survey of Numerical Algorithms that can Solve the Lasso Problems