{"ID":2832793,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.04406","arxiv_id":"2512.04406","title":"A Dual Riemannian ADMM Algorithm for Low-Rank SDPs with Unit Diagonal","abstract":"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.","short_abstract":"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 converge...","url_abs":"https://arxiv.org/abs/2512.04406","url_pdf":"https://arxiv.org/pdf/2512.04406v1","authors":"[\"Jie Wang\",\"Liangbing Hu\",\"Bican Xia\"]","published":"2025-12-04T03:09:59Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}