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arXiv · 1209.6281

On approximations by projections of polytopes with few facets

Alexander E. Litvak·Mark Rudelson·Nicole Tomczak-Jaegermann
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Abstract

We provide an affirmative answer to a problem posed by Barvinok and Veomett, showing that in general an n-dimensional convex body cannot be approximated by a projection of a section of a simplex of a sub-exponential dimension. Moreover, we establish a lower bound of the Banach-Mazur distance between n-dimensional projections of sections of an N-dimensional simplex and a certain convex symmetric body, which is sharp up to a logarithmic factor for all N>n.

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Alexander E. Litvak, Mark Rudelson, Nicole Tomczak-Jaegermann. 2012-09-27. On approximations by projections of polytopes with few facets. https://arxiv.org/abs/1209.6281

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