A Bregman firmly nonexpansive proximal operator for baryconvex optimization
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866908312738463744 |
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| author | Achab, Mastane |
| author_facet | Achab, Mastane |
| contents | We present a generalization of the proximal operator defined through a convex combination of convex objectives, where the coefficients are updated in a minimax fashion. We prove that this new operator is Bregman firmly nonexpansive with respect to a Bregman divergence that combines Euclidean and information geometries; and that its fixed points are given by the critical points of a certain nonconvex function. Finally, we derive the associated continuous flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00928 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Bregman firmly nonexpansive proximal operator for baryconvex optimization Achab, Mastane Optimization and Control Machine Learning We present a generalization of the proximal operator defined through a convex combination of convex objectives, where the coefficients are updated in a minimax fashion. We prove that this new operator is Bregman firmly nonexpansive with respect to a Bregman divergence that combines Euclidean and information geometries; and that its fixed points are given by the critical points of a certain nonconvex function. Finally, we derive the associated continuous flows. |
| title | A Bregman firmly nonexpansive proximal operator for baryconvex optimization |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2411.00928 |