1. Nonconvex flexible sparsity regularization: theory and monotone numerical schemes
- Author
-
Daria Ghilli, Dirk A. Lorenz, and Elena Resmerita
- Subjects
Control and Optimization ,49XX, 65KXX, 90CXX ,Applied Mathematics ,MathematicsofComputing_NUMERICALANALYSIS ,020206 networking & telecommunications ,Numerical Analysis (math.NA) ,010103 numerical & computational mathematics ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,Mathematics - Analysis of PDEs ,Optimization and Control (math.OC) ,FOS: Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Mathematics - Numerical Analysis ,0101 mathematics ,Mathematics - Optimization and Control ,Analysis of PDEs (math.AP) - 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.
- Published
- 2021