# Efficient Solvers for SLOPE in R, Python, Julia, and C++

arXiv: https://arxiv.org/abs/2511.02430 · HTML: https://mlsanity.com/paper/2511.02430/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 81 references that are in the map.
- First posted on arXiv 4 Nov 2025.

## Builds on (most cited first, 19 of 19)

- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [SLOPE - Adaptive variable selection via convex optimization](https://mlsanity.com/paper/1407.3824/) (2014)
- [Mind the duality gap: safer rules for the Lasso](https://mlsanity.com/paper/1505.03410/) (2015)
- [Celer: a Fast Solver for the Lasso with Dual Extrapolation](https://mlsanity.com/paper/1802.07481/) (2018)
- [Benchopt: Reproducible, efficient and collaborative optimization benchmarks](https://mlsanity.com/paper/2206.13424/) (2022)
- [Globally Convergent Type-I Anderson Acceleration for Non-Smooth Fixed-Point Iterations](https://mlsanity.com/paper/1808.03971/) (2018)
- [Beyond L1: Faster and Better Sparse Models with skglm](https://mlsanity.com/paper/2204.07826/) (2022)
- [Group SLOPE - adaptive selection of groups of predictors](https://mlsanity.com/paper/1610.04960/) (2016)
- [The Strong Screening Rule for SLOPE](https://mlsanity.com/paper/2005.03730/) (2020)
- [The biglasso Package: A Memory- and Computation-Efficient Solver for Lasso Model Fitting with Big Data in R](https://mlsanity.com/paper/1701.05936/) (2017)
- [Safe rules for the identification of zeros in the solutions of the SLOPE problem](https://mlsanity.com/paper/2110.11784/) (2021)
- [Sparse-group SLOPE: adaptive bi-level selection with FDR-control](https://mlsanity.com/paper/2305.09467/) (2023)
- [Solving the OSCAR and SLOPE Models Using a Semismooth Newton-Based Augmented Lagrangian Method](https://mlsanity.com/paper/1803.10740/) (2018)
- [Coordinate Descent for SLOPE](https://mlsanity.com/paper/2210.14780/) (2022)
- [Sparse Estimation with Strongly Correlated Variables using Ordered Weighted L1 Regularization](https://mlsanity.com/paper/1409.4005/) (2014)
- [The Hessian Screening Rule](https://mlsanity.com/paper/2104.13026/) (2021)
- [Look-Ahead Screening Rules for the Lasso](https://mlsanity.com/paper/2105.05648/) (2021)
- [The Choice of Normalization Influences Shrinkage in Regularized Regression](https://mlsanity.com/paper/2501.03821/) (2025)
- [Decreasing Weighted Sorted ℓ1 Regularization](https://mlsanity.com/paper/1404.3184/) (2014)

## Abstract (arXiv)

We present a suite of packages in R, Python, Julia, and C++ that efficiently solve the Sorted L-One Penalized Estimation (SLOPE) problem. The packages feature a highly efficient hybrid coordinate descent algorithm that fits generalized linear models (GLMs) and supports a variety of loss functions, including Gaussian, binomial, Poisson, and multinomial logistic regression. Our implementation is designed to be fast, memory-efficient, and flexible. The packages support a variety of data structures (dense, sparse, and out-of-memory matrices) and are designed to efficiently fit the full SLOPE path as well as handle cross-validation of SLOPE models, including the relaxed SLOPE. We present examples of how to use the packages and benchmarks that demonstrate the performance of the packages on both real and simulated data and show that our packages outperform existing implementations of SLOPE in terms of speed.