l1-Norm Minimization with Regula Falsi Type Root Finding Methods

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.

l1 -norm minimization, nonconvex models, Regula-Falsi, root-finding

References in corpus (3)

• L1-Penalization for Mixture Regression Models
• Sparse/Robust Estimation and Kalman Smoothing with Nonsmooth Log-Concave Densities: Modeling, Computation, and Theory
• Variational properties of value functions