In this blog post I give a description of my GSoC 19 student project in a weekly basis. The project took place from May 2019 until August 2019. You can read the proposal here.


Sampling algorithms and volume computation of convex polytopes are very useful in many scientific fields and applications. The package volesti is a C++ package with an R interface which provides three geometric random walks for sampling and two state-of-the-art methods for volume estimation for convex polytopes being the first package providing such a variety of options in geometric statistics. volesti currently scales to a few hundreds dimensions in contrast to other available R packages, as geometry, or C++ package VINCI that both only scale typically up to 15-20 dimensions. Thus it could be an essential tool for a quite large number of scientific applications in convex analysis, economics, biology or statistics, that need fast volume approximation or sampling in high dimensions. However, the possibility to scale from a few hundred to a few thousand dimensions was considered as a very far-reaching goal for many years. The goal of this project is to provide the first ever implementations for sampling and volume computation for convex polytopes in a few thousand dimensions. We exploit some very recent theoretical results that guarantee fast convergence and numerical stability in order to propose an efficient implementation of the current state-of-the-art geometrical random walks, i.e. Hamiltonian Monte Carlo and Vaidya walk. The proposed implementations will be a decisive contribution to other scientific fields as computational geometry, finance and optimization. We hope this project will be a decisive contribution towards the first complete and efficient tool for sampling, volume estimation and geometrical statistics in general and thus, help educational programs, research or even serve as a building block towards an international, interdisciplinary community in geometrical statistics.

Bonding period

Coding period