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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.05316 |
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| _version_ | 1866908408279465984 |
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| author | Yukawa, Masahiro |
| author_facet | Yukawa, Masahiro |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05316 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Continuous Relaxation of Discontinuous Shrinkage Operator: Proximal Inclusion and Conversion Yukawa, Masahiro Optimization and Control 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. |
| title | Continuous Relaxation of Discontinuous Shrinkage Operator: Proximal Inclusion and Conversion |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2409.05316 |