Perturbed Fenchel Duality and Primal-Dual Convergence of First-Order Methods
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908154914144256 |
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| author | Zhao, Tiantian |
| author_facet | Zhao, Tiantian |
| contents | It has been shown that many first-order methods satisfy the perturbed Fenchel duality inequality, which yields a unified derivation of convergence. More first-order methods are discussed in this paper, e.g., dual averaging and bundle method. We show primal-dual convergence of them on convex optimization by proving the perturbed Fenchel duality property. We also propose a single-cut bundle method for saddle problem, and prove its convergence in a similar manner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Perturbed Fenchel Duality and Primal-Dual Convergence of First-Order Methods Zhao, Tiantian Optimization and Control It has been shown that many first-order methods satisfy the perturbed Fenchel duality inequality, which yields a unified derivation of convergence. More first-order methods are discussed in this paper, e.g., dual averaging and bundle method. We show primal-dual convergence of them on convex optimization by proving the perturbed Fenchel duality property. We also propose a single-cut bundle method for saddle problem, and prove its convergence in a similar manner. |
| title | Perturbed Fenchel Duality and Primal-Dual Convergence of First-Order Methods |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2411.09503 |