# A Survey of Numerical Algorithms that can Solve the Lasso Problems

arXiv: https://arxiv.org/abs/2303.03576 · HTML: https://mlsanity.com/paper/2303.03576/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 28 references that are in the map.
- First posted on arXiv 7 Mar 2023.

## Built on by (most cited first, 5 of 5)

- [Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Finance](https://mlsanity.com/paper/2509.03898/) (2025)
- [Strong Screening Rules for Group-based SLOPE Models](https://mlsanity.com/paper/2405.15357/) (2024)
- [Empty SPACE: Cross-Attention Sparsity for Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2605.10198/) (2026)
- [Dual Feature Reduction for the Sparse-group Lasso and its Adaptive Variant](https://mlsanity.com/paper/2405.17094/) (2024)
- [A fast algorithm for solving the lasso problem exactly without homotopy using differential inclusions](https://mlsanity.com/paper/2507.05562/) (2025)

## Abstract (arXiv)

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.