# Convexification with bounded gap for randomly projected quadratic optimization

arXiv: https://arxiv.org/abs/2107.05272 · HTML: https://mlsanity.com/paper/2107.05272/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2021.

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

- [Efficient Optimization with Orthogonality Constraint: a Randomized Riemannian Submanifold Method](https://mlsanity.com/paper/2505.12378/) (2025)
- [Data-driven Projection Generation for Efficiently Solving Heterogeneous Quadratic Programming Problems](https://mlsanity.com/paper/2510.26061/) (2025)

## Abstract (arXiv)

Random projection techniques based on Johnson-Lindenstrauss lemma are used for randomly aggregating the constraints or variables of optimization problems while approximately preserving their optimal values, that leads to smaller-scale optimization problems. D'Ambrosio et al. have applied random projection to a quadratic optimization problem so as to decrease the number of decision variables. Although the problem size becomes smaller, the projected problem will also almost surely be non-convex if the original problem is non-convex, and hence will be hard to solve. In this paper, by focusing on the fact that the level of the non-convexity of a non-convex quadratic optimization problem can be alleviated by random projection, we find an approximate global optimal value of the problem by attributing it to a convex problem with smaller size. To the best of our knowledge, our paper is the first to use random projection for convexification of non-convex optimization problems. We evaluate the approximation error between optimum values of a non-convex optimization problem and its convexified randomly projected problem.