# A Second-Order Method for Strongly Convex L1-Regularization Problems

arXiv: https://arxiv.org/abs/1306.5386 · HTML: https://mlsanity.com/paper/1306.5386/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2013.

## Built on by (most cited first, 2 of 2)

- [Optimal randomized classification trees](https://mlsanity.com/paper/2110.11952/) (2021)
- [SCORE: Approximating Curvature Information under Self-Concordant Regularization](https://mlsanity.com/paper/2112.07344/) (2021)

## Abstract (arXiv)

In this paper a robust second-order method is developed for the solution of strongly convex l1-regularized problems. The main aim is to make the proposed method as inexpensive as possible, while even difficult problems can be efficiently solved. The proposed approach is a primal-dual Newton Conjugate Gradients (pdNCG) method. Convergence properties of pdNCG are studied and worst-case iteration complexity is established. Numerical results are presented on synthetic sparse least-squares problems and real world machine learning problems.