Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.05316 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We present a principled way of deriving a continuous relaxation of a given discontinuous shrinkage operator, which is based on two fundamental results, proximal inclusion and conversion. Using our results, the discontinuous operator is converted, via double inversion, to a continuous operator; more precisely, the associated ``set-valued'' operator is converted to a ``single-valued'' Lipschitz continuous operator. The first illustrative example is the firm shrinkage operator which can be derived as a continuous relaxation of the hard shrinkage operator. We also derive a new operator as a continuous relaxation of the discontinuous shrinkage operator associated with the so-called reversely ordered weighted L1 (ROWL) penalty. Numerical examples demonstrate potential advantages of the continuous relaxation.