Volesti: Volume Approximation and Sampling for Convex Polytopes in R

TL;DR

volesti is an R package offering scalable algorithms for volume estimation and sampling from convex polytopes, enabling high-dimensional computations in various scientific fields.

Contribution

It introduces efficient, scalable algorithms for volume approximation and sampling in R, supporting high-dimensional convex polytopes and three polyhedron types, with new routines not previously available in R.

Findings

Scales to hundreds of dimensions

Handles three types of polyhedra efficiently

Provides novel sampling routines in R

Abstract

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.