A Sweep-Plane Algorithm for Generating Random Tuples in Simple Polytopes

Josef Leydold, Wolfgang Hörmann

Publication: Working/Discussion PaperWU Working Paper

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Abstract

A sweep-plane algorithm by 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. (author's abstract)

Publication series

SeriesPreprint Series / Department of Applied Statistics and Data Processing
Number18

WU Working Paper Series

  • Preprint Series / Department of Applied Statistics and Data Processing

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