Proximity Operators of Perspective Functions with Nonlinear Scaling
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929409713242112 |
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| author | Briceño-Arias, Luis M. Combettes, Patrick L. Silva, Francisco J. |
| author_facet | Briceño-Arias, Luis M. Combettes, Patrick L. Silva, Francisco J. |
| contents | A perspective function is a construction which combines a base function defined on a given space with a nonlinear scaling function defined on another space and which yields a lower semicontinuous convex function on the product space. Since perspective functions are typically nonsmooth, their use in first-order algorithms necessitates the computation of their proximity operator. This paper establishes closed-form expressions for the proximity operator of a perspective function defined on a Hilbert space in terms of a proximity operator involving its base function and one involving its scaling function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_05337 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Proximity Operators of Perspective Functions with Nonlinear Scaling Briceño-Arias, Luis M. Combettes, Patrick L. Silva, Francisco J. Optimization and Control A perspective function is a construction which combines a base function defined on a given space with a nonlinear scaling function defined on another space and which yields a lower semicontinuous convex function on the product space. Since perspective functions are typically nonsmooth, their use in first-order algorithms necessitates the computation of their proximity operator. This paper establishes closed-form expressions for the proximity operator of a perspective function defined on a Hilbert space in terms of a proximity operator involving its base function and one involving its scaling function. |
| title | Proximity Operators of Perspective Functions with Nonlinear Scaling |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2303.05337 |