Solving Linear Programs with Fast Online Learning Algorithms
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866915006421925888 |
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| author | Gao, Wenzhi Ge, Dongdong Sun, Chunlin Ye, Yinyu |
| author_facet | Gao, Wenzhi Ge, Dongdong Sun, Chunlin Ye, Yinyu |
| contents | This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a variable-duplication technique that copies each variable $K$ times and reduces the optimality gap and constraint violation by a factor of $\sqrt{K}$. Furthermore, we show how online algorithms can be effectively integrated into sifting, a column generation scheme for large-scale LPs. Numerical experiments demonstrate that our methods can serve as either an approximate direct solver, or an initialization subroutine for exact LP solving. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_03570 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Solving Linear Programs with Fast Online Learning Algorithms Gao, Wenzhi Ge, Dongdong Sun, Chunlin Ye, Yinyu Optimization and Control Data Structures and Algorithms This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a variable-duplication technique that copies each variable $K$ times and reduces the optimality gap and constraint violation by a factor of $\sqrt{K}$. Furthermore, we show how online algorithms can be effectively integrated into sifting, a column generation scheme for large-scale LPs. Numerical experiments demonstrate that our methods can serve as either an approximate direct solver, or an initialization subroutine for exact LP solving. |
| title | Solving Linear Programs with Fast Online Learning Algorithms |
| topic | Optimization and Control Data Structures and Algorithms |
| url | https://arxiv.org/abs/2107.03570 |