Elastic-Net Regularization: Error estimates and Active Set Methods

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.

Cited by in corpus (9)

• Heuristic parameter-choice rules for convex variational regularization based on error estimates
• The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography
• A Primal Dual Active Set Algorithm with Continuation for Compressed Sensing
• A Two-stage Method for Inverse Medium Scattering
• Elastic-net regularization versus ${\ell }^1$-regularization for linear inverse problems with quasi-sparse solutions
• Beyond convergence rates: Exact recovery with Tikhonov regularization with sparsity constraints
• New Tools for Decomposition of Sea Floor Pressure Data - A Practical Comparison of Modern and Classical Approaches
• Convergence rates for the joint solution of inverse problems with compressed sensing data
• Convergence analysis of a primal-dual optimization-by-continuation algorithm