Sparse Regularization by Smooth Non-separable Non-convex Penalty Function Based on Ultra-discretization Formula
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911173276860416 |
|---|---|
| author | Akaishi, Natsuki Yamada, Koki Yatabe, Kohei |
| author_facet | Akaishi, Natsuki Yamada, Koki Yatabe, Kohei |
| contents | In sparse optimization, the $\ell_{1}$ norm is widely adopted for its convexity, yet it often yields solutions with smaller magnitudes than expected. To mitigate this drawback, various non-convex sparse penalties have been proposed. Some employ non-separability, with ordered weighting as an effective example, to retain large components while suppressing small ones. Motivated by these approaches, we propose ULPENS, a non-convex, non-separable sparsity-inducing penalty function that enables control over the suppression of elements. Derived from the ultra-discretization formula, ULPENS can continuously interpolate between the $\ell_{1}$ norm and a non-convex selective suppressing function by adjusting parameters inherent to the formula. With the formula, ULPENS is smooth, allowing the use of efficient gradient-based optimization algorithms. We establish key theoretical properties of ULPENS and demonstrate its practical effectiveness through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19886 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sparse Regularization by Smooth Non-separable Non-convex Penalty Function Based on Ultra-discretization Formula Akaishi, Natsuki Yamada, Koki Yatabe, Kohei Optimization and Control Signal Processing In sparse optimization, the $\ell_{1}$ norm is widely adopted for its convexity, yet it often yields solutions with smaller magnitudes than expected. To mitigate this drawback, various non-convex sparse penalties have been proposed. Some employ non-separability, with ordered weighting as an effective example, to retain large components while suppressing small ones. Motivated by these approaches, we propose ULPENS, a non-convex, non-separable sparsity-inducing penalty function that enables control over the suppression of elements. Derived from the ultra-discretization formula, ULPENS can continuously interpolate between the $\ell_{1}$ norm and a non-convex selective suppressing function by adjusting parameters inherent to the formula. With the formula, ULPENS is smooth, allowing the use of efficient gradient-based optimization algorithms. We establish key theoretical properties of ULPENS and demonstrate its practical effectiveness through numerical experiments. |
| title | Sparse Regularization by Smooth Non-separable Non-convex Penalty Function Based on Ultra-discretization Formula |
| topic | Optimization and Control Signal Processing |
| url | https://arxiv.org/abs/2509.19886 |