volesti: Volume Approximation and Sampling for Convex Polytopes 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.