Nonconvex flexible sparsity regularization: theory and monotone numerical schemes

2021/11/11 by Ghilli, Daria, Lorenz, Dirk A., Resmerita, Elena · 1 citation
#49XX #65KXX #90CXX #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2111.06281

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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• Sparsity via Hyperpriors: A Theoretical and Algorithmic Study under Empirical Bayes Framework

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