Enhanced computation of the proximity operator for perspective functions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912114531106816 |
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| author | Briceño-Arias, Luis M. Vivar-Vargas, Cristóbal |
| author_facet | Briceño-Arias, Luis M. Vivar-Vargas, Cristóbal |
| contents | In this paper we provide an explicit expression for the proximity operator of a perspective of any proper lower semicontinuous convex function defined on a Hilbert space. Our computation enhances and generalizes known formulae for the case when the Fenchel conjugate of the convex function has open domain or when it is radial. We provide several examples of non-radial functions for which the domain of its conjugate is not open and we compute the proximity operators of their perspectives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_04999 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Enhanced computation of the proximity operator for perspective functions Briceño-Arias, Luis M. Vivar-Vargas, Cristóbal Optimization and Control 46N10, 47J20, 49J53, 49N15, 90C25 In this paper we provide an explicit expression for the proximity operator of a perspective of any proper lower semicontinuous convex function defined on a Hilbert space. Our computation enhances and generalizes known formulae for the case when the Fenchel conjugate of the convex function has open domain or when it is radial. We provide several examples of non-radial functions for which the domain of its conjugate is not open and we compute the proximity operators of their perspectives. |
| title | Enhanced computation of the proximity operator for perspective functions |
| topic | Optimization and Control 46N10, 47J20, 49J53, 49N15, 90C25 |
| url | https://arxiv.org/abs/2305.04999 |