# Privately Solving Linear Programs

arXiv: https://arxiv.org/abs/1402.3631 · HTML: https://mlsanity.com/paper/1402.3631/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2014.

## Built on by (most cited first, 7 of 7)

- [Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism](https://mlsanity.com/paper/2111.12981/) (2021)
- [Multi-Task Differential Privacy Under Distribution Skew](https://mlsanity.com/paper/2302.07975/) (2023)
- [Differential Privacy via Distributionally Robust Optimization](https://mlsanity.com/paper/2304.12681/) (2023)
- [Differentially Private Partial Set Cover with Applications to Facility Location](https://mlsanity.com/paper/2207.10240/) (2022)
- [Faster Sampling from Log-Concave Densities over Polytopes via Efficient Linear Solvers](https://mlsanity.com/paper/2409.04320/) (2024)
- [Differential Privacy for Euclidean Jordan Algebra with Applications to Private Symmetric Cone Programming](https://mlsanity.com/paper/2509.16915/) (2025)
- [Fast-MWEM: Private Data Release in Sublinear Time](https://mlsanity.com/paper/2602.03732/) (2026)

## Abstract (arXiv)

In this paper, we initiate the systematic study of solving linear programs under differential privacy. The first step is simply to define the problem: to this end, we introduce several natural classes of private linear programs that capture different ways sensitive data can be incorporated into a linear program. For each class of linear programs we give an efficient, differentially private solver based on the multiplicative weights framework, or we give an impossibility result.