Solving separable convex optimization problems: Faster prediction-correction framework
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911769832718336 |
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| author | Zhang, Tao Xia, Yong Li, Shiru |
| author_facet | Zhang, Tao Xia, Yong Li, Shiru |
| contents | He and Yuan's prediction-correction framework [SIAM J. Numer. Anal. 50: 700-709, 2012] is able to provide convergent algorithms for solving separable convex optimization problems at a rate of $O(1/t)$ ($t$ represents iteration times) in both ergodic (the average of iteration) and pointwise senses. This paper presents a faster prediction-correction framework at a rate of $O(1/t)$ in the non-ergodic sense (the last iteration) and $O(1/t^2)$ in the pointwise sense. Based the faster prediction-correction framework, we give three faster algorithms which enjoy $O(1/t)$ in the non-ergodic sense of primal-dual gap and $O(1/t^2)$ in the pointwise sense. The first algorithm updates dual variable twice when solving two-block separable convex optimization with equality linear constraints. The second algorithm solves multi-block separable convex optimization problems with linear equality constraints in Gauss-Seidel way. The third algorithm solves minmax problems with larger step sizes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02465 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Solving separable convex optimization problems: Faster prediction-correction framework Zhang, Tao Xia, Yong Li, Shiru Optimization and Control He and Yuan's prediction-correction framework [SIAM J. Numer. Anal. 50: 700-709, 2012] is able to provide convergent algorithms for solving separable convex optimization problems at a rate of $O(1/t)$ ($t$ represents iteration times) in both ergodic (the average of iteration) and pointwise senses. This paper presents a faster prediction-correction framework at a rate of $O(1/t)$ in the non-ergodic sense (the last iteration) and $O(1/t^2)$ in the pointwise sense. Based the faster prediction-correction framework, we give three faster algorithms which enjoy $O(1/t)$ in the non-ergodic sense of primal-dual gap and $O(1/t^2)$ in the pointwise sense. The first algorithm updates dual variable twice when solving two-block separable convex optimization with equality linear constraints. The second algorithm solves multi-block separable convex optimization problems with linear equality constraints in Gauss-Seidel way. The third algorithm solves minmax problems with larger step sizes. |
| title | Solving separable convex optimization problems: Faster prediction-correction framework |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2304.02465 |