Elastic-Net Regularization: Error estimates and Active Set Methods

TL;DR

This paper analyzes the theoretical stability and convergence of elastic-net regularization, combining l^1 and l^2 penalties, and introduces efficient active set algorithms with numerical validation.

Contribution

It provides new stability and convergence results for elastic-net regularization and proposes active set algorithms with proven convergence properties.

Findings

Stability and consistency of elastic-net minimizers established.

Convergence rates for parameter choice rules derived.

Numerical experiments demonstrate algorithm effectiveness.

Abstract

This paper investigates theoretical properties and efficient numerical algorithms for the so-called elastic-net regularization originating from statistics, which enforces simultaneously l^1 and l^2 regularization. The stability of the minimizer and its consistency are studied, and convergence rates for both a priori and a posteriori parameter choice rules are established. Two iterative numerical algorithms of active set type are proposed, and their convergence properties are discussed. Numerical results are presented to illustrate the features of the functional and algorithms.