# Efficient Rank Minimization to Tighten Semidefinite Programming for Unconstrained Binary Quadratic Optimization

arXiv: https://arxiv.org/abs/1708.01690 · HTML: https://mlsanity.com/paper/1708.01690/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2017.

## Built on by (most cited first, 1 of 1)

- [Inference and Optimization for Engineering and Physical Systems](https://mlsanity.com/paper/2208.13880/) (2022)

## Abstract (arXiv)

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.