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Nonconvex flexible sparsity regularization: theory and monotone numerical schemes
- Source :
- Optimization. 71:1117-1149
- Publication Year :
- 2021
- Publisher :
- Informa UK Limited, 2021.
-
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.
- 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)
Subjects
Details
- ISSN :
- 10294945 and 02331934
- Volume :
- 71
- Database :
- OpenAIRE
- Journal :
- Optimization
- Accession number :
- edsair.doi.dedup.....f9661b9dcdb06d82b44077271c762086