# A Second-Order Method for Convex ℓ1-Regularized Optimization with Active Set Prediction

arXiv: https://arxiv.org/abs/1505.04315 · HTML: https://mlsanity.com/paper/1505.04315/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2015.

## Built on by (most cited first, 1 of 1)

- [Alternating Iteratively Reweighted ℓ1 and Subspace Newton Algorithms for Nonconvex Sparse Optimization](https://mlsanity.com/paper/2407.17216/) (2024)

## Abstract (arXiv)

We describe an active-set method for the minimization of an objective function φ that is the sum of a smooth convex function and an ℓ1-regularization term. A distinctive feature of the method is the way in which active-set identification and second-order subspace minimization steps are integrated to combine the predictive power of the two approaches. At every iteration, the algorithm selects a candidate set of free and fixed variables, performs an (inexact) subspace phase, and then assesses the quality of the new active set. If it is not judged to be acceptable, then the set of free variables is restricted and a new active-set prediction is made. We establish global convergence for our approach, and compare the new method against the state-of-the-art code LIBLINEAR.