Nonconvex flexible sparsity regularization: theory and monotone numerical schemes

Daria Ghilli; Dirk A. Lorenz; Elena Resmerita

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arXiv · 2111.06281

Nonconvex flexible sparsity regularization: theory and monotone numerical schemes

Daria Ghilli·Dirk A. Lorenz·Elena Resmerita

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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.

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BibTeX RIS

Daria Ghilli, Dirk A. Lorenz, Elena Resmerita. 2021-11-11. Nonconvex flexible sparsity regularization: theory and monotone numerical schemes. https://arxiv.org/abs/2111.06281

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