Nonconvex flexible sparsity regularization: theory and monotone numerical schemes

11/11/2021
by   Daria Ghilli, et al.
0

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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset