Jin, Bangti; Lorenz, Dirk A.; Schiffler, Stefan Elastic-net regularization: error estimates and active set methods. (English) Zbl 1188.49026 Inverse Probl. 25, No. 11, Article ID 115022, 26 p. (2009). Summary: This paper investigates theoretical properties and efficient numerical algorithms for the so-called elastic-net regularization originating from statistics, which enforces simultaneously \(\ell^1\) and \(\ell^2\) 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 the algorithms. Cited in 1 ReviewCited in 26 Documents MSC: 49K40 Sensitivity, stability, well-posedness 49M30 Other numerical methods in calculus of variations (MSC2010) Keywords:numerical algorithms; elastic-net regularization; stability of the minimizer Software:Regularization tools PDFBibTeX XMLCite \textit{B. Jin} et al., Inverse Probl. 25, No. 11, Article ID 115022, 26 p. (2009; Zbl 1188.49026) Full Text: DOI arXiv