# SDP-quality bounds via convex quadratic relaxations for global optimization of mixed-integer quadratic programs

arXiv: https://arxiv.org/abs/2106.13721 · HTML: https://mlsanity.com/paper/2106.13721/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2021.

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

- [Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part I: Definitions & Basic Properties](https://mlsanity.com/paper/2208.03622/) (2022)
- [A Penalty-Based Guardrail Algorithm for Non-Decreasing Optimization with Inequality Constraints](https://mlsanity.com/paper/2405.01984/) (2024)

## Abstract (arXiv)

We consider the global optimization of nonconvex mixed-integer quadratic programs with linear equality constraints. In particular, we present a new class of convex quadratic relaxations which are derived via quadratic cuts. To construct these quadratic cuts, we solve a separation problem involving a linear matrix inequality with a special structure that allows the use of specialized solution algorithms. Our quadratic cuts are nonconvex, but define a convex feasible set when intersected with the equality constraints. We show that our relaxations are an outer-approximation of a semi-infinite convex program which under certain conditions is equivalent to a well-known semidefinite program relaxation. The new relaxations are implemented in the global optimization solver BARON, and tested by conducting numerical experiments on a large collection of problems. Results demonstrate that, for our test problems, these relaxations lead to a significant improvement in the performance of BARON.