Forward-Backward algorithms for weakly convex problems
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916295999488000 |
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| author | Bednarczuk, Ewa Bruccola, Giovanni Scrivanti, Gabriele Tran, The Hung |
| author_facet | Bednarczuk, Ewa Bruccola, Giovanni Scrivanti, Gabriele Tran, The Hung |
| contents | We investigate the convergence properties of exact and inexact forward-backward algorithms to minimise the sum of two weakly convex functions defined on a Hilbert space, where one has a Lipschitz-continuous gradient. We show that the exact forward-backward algorithm converges strongly to a global solution, provided that the objective function satisfies a sharpness condition. For the inexact forward-backward algorithm, the same condition ensures that the distance from the iterates to the solution set approaches a positive threshold depending on the accuracy level of the proximal computations. As an application of the considered setting, we provide numerical experiments related to discrete tomography. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_14021 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Forward-Backward algorithms for weakly convex problems Bednarczuk, Ewa Bruccola, Giovanni Scrivanti, Gabriele Tran, The Hung Optimization and Control 90C30 90C26 90C51 65K10 52A01 We investigate the convergence properties of exact and inexact forward-backward algorithms to minimise the sum of two weakly convex functions defined on a Hilbert space, where one has a Lipschitz-continuous gradient. We show that the exact forward-backward algorithm converges strongly to a global solution, provided that the objective function satisfies a sharpness condition. For the inexact forward-backward algorithm, the same condition ensures that the distance from the iterates to the solution set approaches a positive threshold depending on the accuracy level of the proximal computations. As an application of the considered setting, we provide numerical experiments related to discrete tomography. |
| title | Forward-Backward algorithms for weakly convex problems |
| topic | Optimization and Control 90C30 90C26 90C51 65K10 52A01 |
| url | https://arxiv.org/abs/2303.14021 |