Efficient Rank Minimization to Tighten Semidefinite Programming for Unconstrained Binary Quadratic Optimization
Optimization and Control
2021-12-07 v1 Computational Complexity
Abstract
We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to achieve a lower rank solution. This procedure is computationally efficient as it does not require projecting on the cone of positive-semidefinite matrices. Its performance in terms of objective improvement and rank reduction is tested over multiple graphs of large-scale Gset graph collection and over binary optimization problems from the Biq Mac collection.
Cite
@article{arxiv.1708.01690,
title = {Efficient Rank Minimization to Tighten Semidefinite Programming for Unconstrained Binary Quadratic Optimization},
author = {Roman Pogodin and Mikhail Krechetov and Yury Maximov},
journal= {arXiv preprint arXiv:1708.01690},
year = {2021}
}