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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2601.19038 |
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| _version_ | 1866908790677307392 |
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| author | Chen, Long Luo, Hao Wei, Jingrong Xu, Zeyi Yao, Yuan |
| author_facet | Chen, Long Luo, Hao Wei, Jingrong Xu, Zeyi Yao, Yuan |
| contents | Mirror descent uses the mirror function to encode geometry and constraints, improving convergence while preserving feasibility. Accelerated Mirror Descent Methods (Acc-MD) are derived from a discretization of an accelerated mirror ODE system using a variable--operator splitting framework. A geometric assumption, termed the Generalized Cauchy-Schwarz (GCS) condition, is introduced to quantify the compatibility between the objective and the mirror geometry, under which the first accelerated linear convergence for Acc-MD on a broad class of problems is established. Numerical experiments on smooth and composite optimization tasks demonstrate that Acc-MD consistently outperforms existing accelerated variants, both theoretically and empirically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19038 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Accelerated Mirror Descent Method through Variable and Operator Splitting Chen, Long Luo, Hao Wei, Jingrong Xu, Zeyi Yao, Yuan Optimization and Control Mirror descent uses the mirror function to encode geometry and constraints, improving convergence while preserving feasibility. Accelerated Mirror Descent Methods (Acc-MD) are derived from a discretization of an accelerated mirror ODE system using a variable--operator splitting framework. A geometric assumption, termed the Generalized Cauchy-Schwarz (GCS) condition, is introduced to quantify the compatibility between the objective and the mirror geometry, under which the first accelerated linear convergence for Acc-MD on a broad class of problems is established. Numerical experiments on smooth and composite optimization tasks demonstrate that Acc-MD consistently outperforms existing accelerated variants, both theoretically and empirically. |
| title | Accelerated Mirror Descent Method through Variable and Operator Splitting |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.19038 |