# Private Optimization Without Constraint Violations

arXiv: https://arxiv.org/abs/2007.01181 · HTML: https://mlsanity.com/paper/2007.01181/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2020.

## Built on by (most cited first, 3 of 3)

- [Private estimation algorithms for stochastic block models and mixture models](https://mlsanity.com/paper/2301.04822/) (2023)
- [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)

## Abstract (arXiv)

We study the problem of differentially private optimization with linear constraints when the right-hand-side of the constraints depends on private data. This type of problem appears in many applications, especially resource allocation. Previous research provided solutions that retained privacy but sometimes violated the constraints. In many settings, however, the constraints cannot be violated under any circumstances. To address this hard requirement, we present an algorithm that releases a nearly-optimal solution satisfying the constraints with probability 1. We also prove a lower bound demonstrating that the difference between the objective value of our algorithm's solution and the optimal solution is tight up to logarithmic factors among all differentially private algorithms. We conclude with experiments demonstrating that our algorithm can achieve nearly optimal performance while preserving privacy.