Box-constrained L0 Bregman-relaxations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909542682460160 |
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| author | Essafri, Mhamed Calatroni, Luca Soubies, Emmanuel |
| author_facet | Essafri, Mhamed Calatroni, Luca Soubies, Emmanuel |
| contents | Regularization using the L0 pseudo-norm is a common approach to promote sparsity, with widespread applications in machine learning and signal processing. However, solving such problems is known to be NP-hard. Recently, the L0 Bregman relaxation (B-rex) has been introduced as a continuous, non-convex approximation of the L0 pseudo-norm. Replacing the L0 term with B-rex leads to exact continuous relaxations that preserve the global optimum while simplifying the optimization landscape, making non-convex problems more tractable for algorithmic approaches. In this paper, we focus on box-constrained exact continuous Bregman relaxations of L0-regularized criteria with general data terms, including least-squares, logistic regression, and Kullback-Leibler fidelities. Experimental results on synthetic data, compared with Branch-and-Bound methods, demonstrate the effectiveness of the proposed relaxations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15083 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Box-constrained L0 Bregman-relaxations Essafri, Mhamed Calatroni, Luca Soubies, Emmanuel Optimization and Control Regularization using the L0 pseudo-norm is a common approach to promote sparsity, with widespread applications in machine learning and signal processing. However, solving such problems is known to be NP-hard. Recently, the L0 Bregman relaxation (B-rex) has been introduced as a continuous, non-convex approximation of the L0 pseudo-norm. Replacing the L0 term with B-rex leads to exact continuous relaxations that preserve the global optimum while simplifying the optimization landscape, making non-convex problems more tractable for algorithmic approaches. In this paper, we focus on box-constrained exact continuous Bregman relaxations of L0-regularized criteria with general data terms, including least-squares, logistic regression, and Kullback-Leibler fidelities. Experimental results on synthetic data, compared with Branch-and-Bound methods, demonstrate the effectiveness of the proposed relaxations. |
| title | Box-constrained L0 Bregman-relaxations |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.15083 |