A Tuning-Free Primal-Dual Splitting Algorithm for Large-Scale Semidefinite Programming
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911768891097088 |
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| author | Wang, Yinjun Lan, Haixiang Ye, Yinyu |
| author_facet | Wang, Yinjun Lan, Haixiang Ye, Yinyu |
| contents | This paper proposes and analyzes a tuning-free variant of Primal-Dual Hybrid Gradient (PDHG), and investigates its effectiveness for solving large-scale semidefinite programming (SDP). The core idea is based on the combination of two seemingly unrelated results: (1) the equivalence of PDHG and Douglas-Rachford splitting (DRS); (2) the asymptotic convergence of non-stationary DRS. This combination provides a unified approach to analyze the convergence of generic adaptive PDHG, including the proposed tuning-free algorithm and various existing ones. Numerical experiments are conducted to show the performance of our algorithm, highlighting its superior convergence speed and robustness in the context of SDP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00311 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Tuning-Free Primal-Dual Splitting Algorithm for Large-Scale Semidefinite Programming Wang, Yinjun Lan, Haixiang Ye, Yinyu Optimization and Control This paper proposes and analyzes a tuning-free variant of Primal-Dual Hybrid Gradient (PDHG), and investigates its effectiveness for solving large-scale semidefinite programming (SDP). The core idea is based on the combination of two seemingly unrelated results: (1) the equivalence of PDHG and Douglas-Rachford splitting (DRS); (2) the asymptotic convergence of non-stationary DRS. This combination provides a unified approach to analyze the convergence of generic adaptive PDHG, including the proposed tuning-free algorithm and various existing ones. Numerical experiments are conducted to show the performance of our algorithm, highlighting its superior convergence speed and robustness in the context of SDP. |
| title | A Tuning-Free Primal-Dual Splitting Algorithm for Large-Scale Semidefinite Programming |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2402.00311 |