Optimal Subgradient Methods for Lipschitz Convex Optimization with Error Bounds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911321956548608 |
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| author | Wang, Alex L. |
| author_facet | Wang, Alex L. |
| contents | We study the iteration complexity of Lipschitz convex optimization problems satisfying a general error bound. We show that for this class of problems, subgradient descent with either Polyak stepsizes or decaying stepsizes achieves minimax optimal convergence guarantees for decreasing distance-to-optimality. The main contribution is a novel lower-bounding argument that produces hard functions simultaneously satisfying zero-chain conditions and global error bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Subgradient Methods for Lipschitz Convex Optimization with Error Bounds Wang, Alex L. Optimization and Control 90C60, 90C25, 90C30 We study the iteration complexity of Lipschitz convex optimization problems satisfying a general error bound. We show that for this class of problems, subgradient descent with either Polyak stepsizes or decaying stepsizes achieves minimax optimal convergence guarantees for decreasing distance-to-optimality. The main contribution is a novel lower-bounding argument that produces hard functions simultaneously satisfying zero-chain conditions and global error bounds. |
| title | Optimal Subgradient Methods for Lipschitz Convex Optimization with Error Bounds |
| topic | Optimization and Control 90C60, 90C25, 90C30 |
| url | https://arxiv.org/abs/2512.13863 |