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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.19886 |
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Table of 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.