Nonconvex flexible sparsity regularization: theory and monotone numerical schemes

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 numerical perspectives. Namely, we show convergence the method establish properties couple majorization approaches for associated problems. also test monotone algorithm an academic example where is M matrix, on time-dependent optimal control problem, pointing out advantages employing variable penalties over fixed penalty.