On the diameter of subgradient sequences in o-minimal structures
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914563878813696 |
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| author | Lai, Lexiao Song, Mingzhi |
| author_facet | Lai, Lexiao Song, Mingzhi |
| contents | We study subgradient sequences of locally Lipschitz functions definable in a polynomially bounded o-minimal structure. We show that the diameter of any subgradient sequence is related to the variation in function values, with error terms dominated by a double summation of step sizes. Consequently, we prove that bounded subgradient sequences converge if the step sizes are of order $1/k$. The proof uses Lipschitz $L$-regular stratifications in o-minimal structures to analyze subgradient sequences via their projections onto different strata. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06868 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the diameter of subgradient sequences in o-minimal structures Lai, Lexiao Song, Mingzhi Optimization and Control Dynamical Systems 65K10 We study subgradient sequences of locally Lipschitz functions definable in a polynomially bounded o-minimal structure. We show that the diameter of any subgradient sequence is related to the variation in function values, with error terms dominated by a double summation of step sizes. Consequently, we prove that bounded subgradient sequences converge if the step sizes are of order $1/k$. The proof uses Lipschitz $L$-regular stratifications in o-minimal structures to analyze subgradient sequences via their projections onto different strata. |
| title | On the diameter of subgradient sequences in o-minimal structures |
| topic | Optimization and Control Dynamical Systems 65K10 |
| url | https://arxiv.org/abs/2511.06868 |