# Fix and Bound: An efficient approach for solving large-scale quadratic programming problems with box constraints

arXiv: https://arxiv.org/abs/2211.08911 · HTML: https://mlsanity.com/paper/2211.08911/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2022.

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

- [Exact and Heuristic Algorithms for Constrained Biclustering](https://mlsanity.com/paper/2508.05493/) (2025)

## Abstract (arXiv)

In this paper, we propose a branch-and-bound algorithm for solving nonconvex quadratic programming problems with box constraints (BoxQP). Our approach combines existing tools, such as semidefinite programming (SDP) bounds strengthened through valid inequalities, with a new class of optimality-based linear cuts which leads to variable fixing. The most important effect of fixing the value of some variables is the size reduction along the branch-and-bound tree, allowing to compute bounds by solving SDPs of smaller dimension. Extensive computational experiments over large dimensional (up to n=200) test instances show that our method is the state-of-the-art solver on large-scale BoxQPs. Furthermore, we test the proposed approach on the class of binary QP problems, where it exhibits competitive performance with state-of-the-art solvers.