Nonconvex flexible sparsity regularization: theory and monotone numerical schemes. (3rd April 2022)

• Record Type: Journal Article
• Authors: Ghilli, Daria; Lorenz, Dirk A.; Resmerita, Elena
• Is Part Of: Optimization. Volume 71:Number 4(2022)
• Page Start: 1117
• Page End: 1149
• Publication Date: 2022-04-03
• Subjects: Sparsity -- variational regularization -- reweighted minimization; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.2011869
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and numerical perspectives. Namely, we show convergence of the regularization method and establish convergence properties of a couple of majorization approaches for the associated nonconvex problems. We also test a monotone algorithm for an academic example where the operator is an M matrix, and on a time-dependent optimal control problem, pointing out the advantages of employing variable penalties over a fixed penalty.