When Does Primal Interior Point Method Beat Primal-dual in Linear Optimization?
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912131832610816 |
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| author | Gao, Wenzhi Liu, Huikang Ye, Yinyu Udell, Madeleine |
| author_facet | Gao, Wenzhi Liu, Huikang Ye, Yinyu Udell, Madeleine |
| contents | The primal-dual interior point method (IPM) is widely regarded as the most efficient IPM variant for linear optimization. In this paper, we demonstrate that the improved stability of the pure primal IPM can allow speedups relative to a primal-dual solver, particularly as the IPM approaches convergence. The stability of the primal scaling matrix makes it possible to accelerate each primal IPM step using fast preconditioned iterative solvers for the normal equations. Crucially, we identify properties of the central path that make it possible to stabilize the normal equations. Experiments on benchmark datasets demonstrate the efficiency of primal IPM and showcase its potential for practical applications in linear optimization and beyond. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16015 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | When Does Primal Interior Point Method Beat Primal-dual in Linear Optimization? Gao, Wenzhi Liu, Huikang Ye, Yinyu Udell, Madeleine Optimization and Control The primal-dual interior point method (IPM) is widely regarded as the most efficient IPM variant for linear optimization. In this paper, we demonstrate that the improved stability of the pure primal IPM can allow speedups relative to a primal-dual solver, particularly as the IPM approaches convergence. The stability of the primal scaling matrix makes it possible to accelerate each primal IPM step using fast preconditioned iterative solvers for the normal equations. Crucially, we identify properties of the central path that make it possible to stabilize the normal equations. Experiments on benchmark datasets demonstrate the efficiency of primal IPM and showcase its potential for practical applications in linear optimization and beyond. |
| title | When Does Primal Interior Point Method Beat Primal-dual in Linear Optimization? |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2411.16015 |