A sweep-plane algorithm for generating random tuples in simple polytopes

Abstract. A sweep-plane algorithm of Lawrence for convex polytope computation is adapted to generate random tuples on simple polytopes. In our method an affine hyperplane is swept through the given polytope until a random fraction (sampled from a proper univariate distribution) of the volume of the polytope is covered. Then the intersection of the plane with the polytope is a simple polytope with smaller dimension. In the second part we apply this method to construct a black-box algorithm for log-concave and T -concave multivariate distributions by means of transformed density rejection.

• Type: Journal
• Year: 1998
• Where: MOC
• Authors: Josef Leydold, Wolfgang Hörmann
• Keywords: Convex Polytope Computation, MOC 1998, Polytope, Simple Polytope