# l1-Norm Minimization with Regula Falsi Type Root Finding Methods

arXiv: https://arxiv.org/abs/2105.00244 · HTML: https://mlsanity.com/paper/2105.00244/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 27 references that are in the map.
- First posted on arXiv 1 May 2021.

## Builds on (most cited first, 2 of 2)

- [Level-set methods for convex optimization](https://mlsanity.com/paper/1602.01506/) (2016)
- [Sparse/Robust Estimation and Kalman Smoothing with Nonsmooth Log-Concave Densities: Modeling, Computation, and Theory](https://mlsanity.com/paper/1301.4566/) (2013)

## Abstract (arXiv)

Sparse level-set formulations allow practitioners to find the minimum 1-norm solution subject to likelihood constraints. Prior art requires this constraint to be convex. In this letter, we develop an efficient approach for nonconvex likelihoods, using Regula Falsi root-finding techniques to solve the level-set formulation. Regula Falsi methods are simple, derivative-free, and efficient, and the approach provably extends level-set methods to the broader class of nonconvex inverse problems. Practical performance is illustrated using l1-regularized Student's t inversion, which is a nonconvex approach used to develop outlier-robust formulations.