volesti

VolEsti is an open-source software library for volume estimation and uniform sampling of convex polytopes in high dimensions. It targets problems in computational geometry, statistics, and machine learning by providing algorithms to compute or approximate the volume of convex bodies and to generate random points uniformly inside polytopes.

The library implements volume estimation methods for various convex bodies and supports several representations of polytopes, including both H-representation (half-spaces) and V-representation (vertices). It includes random-walk based sampling algorithms, such as Hit-and-Run and related Monte Carlo methods, to produce near-uniform samples from inside a polytope. It also offers utilities for polytope manipulation and analysis, and is designed to be efficient and numerically robust in higher dimensions.

VolEsti is implemented in C++ with performance-oriented design and provides interfaces or bindings for higher-level languages to facilitate integration into research workflows. It is distributed under an open-source license and hosted on a public repository, with documentation, examples, and benchmarks available to users. The project is maintained by an active community of researchers and developers, and it continuously adds new algorithms and improvements.

Common applications include volume computation for high-dimensional polytopes, probabilistic modeling and Bayesian computation requiring sampling from constrained spaces, and algorithmic testing in optimization and computational geometry. See also: convex geometry, volume estimation, Monte Carlo methods, Hit-and-Run.