A Dual Riemannian ADMM Algorithm for Low-Rank SDPs with Unit Diagonal
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911301513510912 |
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| author | Wang, Jie Hu, Liangbing Xia, Bican |
| author_facet | Wang, Jie Hu, Liangbing Xia, Bican |
| contents | This paper proposes a dual Riemannian alternating direction method of multipliers (ADMM) for solving low-rank semidefinite programs with unit diagonal constraints. We recast the ADMM subproblem as a Riemannian optimization problem over the oblique manifold by performing the Burer-Monteiro factorization. Global convergence of the algorithm is established assuming that the subproblem is solved to certain optimality. Numerical experiments demonstrate the excellent performance of the algorithm. It outperforms, by a significant margin, a few advanced SDP solvers (MOSEK, COPT, SDPNAL+, ManiSDP) in terms of accuracy, efficiency, and scalability on second-order SDP relaxations of dense and sparse binary quadratic programs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_04406 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Dual Riemannian ADMM Algorithm for Low-Rank SDPs with Unit Diagonal Wang, Jie Hu, Liangbing Xia, Bican Optimization and Control Primary, 90C22, Secondary, 90C23, 90C30 This paper proposes a dual Riemannian alternating direction method of multipliers (ADMM) for solving low-rank semidefinite programs with unit diagonal constraints. We recast the ADMM subproblem as a Riemannian optimization problem over the oblique manifold by performing the Burer-Monteiro factorization. Global convergence of the algorithm is established assuming that the subproblem is solved to certain optimality. Numerical experiments demonstrate the excellent performance of the algorithm. It outperforms, by a significant margin, a few advanced SDP solvers (MOSEK, COPT, SDPNAL+, ManiSDP) in terms of accuracy, efficiency, and scalability on second-order SDP relaxations of dense and sparse binary quadratic programs. |
| title | A Dual Riemannian ADMM Algorithm for Low-Rank SDPs with Unit Diagonal |
| topic | Optimization and Control Primary, 90C22, Secondary, 90C23, 90C30 |
| url | https://arxiv.org/abs/2512.04406 |