# A Fast Semidefinite Approach to Solving Binary Quadratic Problems

arXiv: https://arxiv.org/abs/1304.0840 · HTML: https://mlsanity.com/paper/1304.0840/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2013.

## Built on by (most cited first, 2 of 2)

- [Projection-free Graph-based Classifier Learning using Gershgorin Disc Perfect Alignment](https://mlsanity.com/paper/2106.01642/) (2021)
- [Unfolding Projection-free SDP Relaxation of Binary Graph Classifier via GDPA Linearization](https://mlsanity.com/paper/2109.04697/) (2021)

## Abstract (arXiv)

Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own advantages and disadvantages. Spectral relaxation is simple and easy to implement, but its bound is loose. Semidefinite relaxation has a tighter bound, but its computational complexity is high for large scale problems. We present a new SDP formulation for BQPs, with two desirable properties. First, it has a similar relaxation bound to conventional SDP formulations. Second, compared with conventional SDP methods, the new SDP formulation leads to a significantly more efficient and scalable dual optimization approach, which has the same degree of complexity as spectral methods. Extensive experiments on various applications including clustering, image segmentation, co-segmentation and registration demonstrate the usefulness of our SDP formulation for solving large-scale BQPs.