Nonconvex flexible sparsity regularization: theory and monotone numerical schemes

11/11/2021

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by   Daria Ghilli, et al.

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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.