# On obtaining the convex hull of quadratic inequalities via aggregations

arXiv: https://arxiv.org/abs/2106.12629 · HTML: https://mlsanity.com/paper/2106.12629/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2021.

## 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 classical approach for obtaining valid inequalities for a set involves weighted aggregations of the inequalities that describe such set. When the set is described by linear inequalities, thanks to the Farkas lemma, we know that every valid inequality can be obtained using aggregations. When the inequalities describing the set are two quadratics, Yildiran showed that the convex hull of the set is given by at most two aggregated inequalities. In this work, we study the case of a set described by three or more quadratic inequalities. We show that, under technical assumptions, the convex hull of a set described by three quadratic inequalities can be obtained via (potentially infinitely many) aggregated inequalities. We also show, through counterexamples, that it is unlikely to have a similar result if either the technical conditions are relaxed, or if we consider four or more inequalities.