l1-Norm Minimization with Regula Falsi Type Root Finding Methods
Optimization and Control
2021-11-24 v1 Computation
Machine Learning
Abstract
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.
Cite
@article{arxiv.2105.00244,
title = {l1-Norm Minimization with Regula Falsi Type Root Finding Methods},
author = {Metin Vural and Aleksandr Y. Aravkin and Sławomir Stan'czak},
journal= {arXiv preprint arXiv:2105.00244},
year = {2021}
}
Comments
l1 -norm minimization, nonconvex models, Regula-Falsi, root-finding