# Volesti: Volume Approximation and Sampling for Convex Polytopes in R

arXiv: https://arxiv.org/abs/2007.01578 · HTML: https://mlsanity.com/paper/2007.01578/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2020.

## Built on by (most cited first, 6 of 6)

- [Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space](https://mlsanity.com/paper/2202.01908/) (2022)
- [Convergence of the Riemannian Langevin Algorithm](https://mlsanity.com/paper/2204.10818/) (2022)
- [Enhancing SMT-based Weighted Model Integration by Structure Awareness](https://mlsanity.com/paper/2302.06188/) (2023)
- [Efficient computation of the volume of a polytope in high-dimensions using Piecewise Deterministic Markov Processes](https://mlsanity.com/paper/2202.09129/) (2022)
- [Tukey Depth Mechanisms for Practical Private Mean Estimation](https://mlsanity.com/paper/2502.18698/) (2025)
- [Improving Stochastic Action-Constrained Reinforcement Learning via Truncated Distributions](https://mlsanity.com/paper/2511.22406/) (2025)

## Abstract (arXiv)

Sampling from high dimensional distributions and volume approximation of convex bodies are fundamental operations that appear in optimization, finance, engineering, artificial intelligence and machine learning. In this paper we present volesti, an R package that provides efficient, scalable algorithms for volume estimation, uniform and Gaussian sampling from convex polytopes. volesti scales to hundreds of dimensions, handles efficiently three different types of polyhedra and provides non existing sampling routines to R. We demonstrate the power of volesti by solving several challenging problems using the R language.