Geodesic walks in polytopes

@article{Lee2016GeodesicWI,
  title={Geodesic walks in polytopes},
  author={Yin Tat Lee and Santosh S. Vempala},
  journal={ArXiv},
  year={2016},
  volume={abs/1606.04696}
}
We introduce the geodesic walk for sampling Riemannian manifolds and apply it to the problem of generating uniform random points from the interior of polytopes in R^n specified by m inequalities. The walk is a discrete-time simulation of a stochastic differential equation (SDE) on the Riemannian manifold equipped with the metric induced by the Hessian of a convex function; each step is the solution of an ordinary differential equation (ODE). The resulting sampling algorithm for polytopes mixes… CONTINUE READING
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