A Dual Riemannian ADMM Algorithm for Low-Rank SDPs with Unit Diagonal

Fuente: arXiv
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Main Authors: Wang, Jie, Hu, Liangbing, Xia, Bican
Format: Preprint
Published: 2025
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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
id 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