# The convex hull of a quadratic constraint over a polytope

arXiv: https://arxiv.org/abs/1812.10160 · HTML: https://mlsanity.com/paper/1812.10160/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2018.

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

- [On the Exactness of Dantzig-Wolfe Relaxation for Rank Constrained Optimization Problems](https://mlsanity.com/paper/2210.16191/) (2022)

## Abstract (arXiv)

A quadratically constrained quadratic program (QCQP) is an optimization problem in which the objective function is a quadratic function and the feasible region is defined by quadratic constraints. Solving non-convex QCQP to global optimality is a well-known NP-hard problem and a traditional approach is to use convex relaxations and branch-and-bound algorithms. This paper makes a contribution in this direction by showing that the exact convex hull of a general quadratic equation intersected with any bounded polyhedron is second-order cone representable. We present a simple constructive proof of this result.