A note on the convergence of deterministic gradient sampling in nonsmooth optimization
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911771812429824 |
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| author | Gebken, Bennet |
| author_facet | Gebken, Bennet |
| contents | Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12032 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on the convergence of deterministic gradient sampling in nonsmooth optimization Gebken, Bennet Optimization and Control 49J52, 90C26 Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions. |
| title | A note on the convergence of deterministic gradient sampling in nonsmooth optimization |
| topic | Optimization and Control 49J52, 90C26 |
| url | https://arxiv.org/abs/2312.12032 |