Abstract
We describe an explicit construction of a linear projection of a symmetric conical section of the n-dimensional cube onto a (1+e)-isomorphic version of the Euclidean ball of proportional dimension, or more generally onto a (1+e)-isomorphic image of an lpm-ball. Allowing non-linear projections (of logarithmic polynomial nonlinearity) we may even project the full n-dimensional cube onto the same images. This is done by gluing together explicit projections onto two-dimensional spaces, interpreting and modifying a paper of Ben-Tal and Nemirowski on polynomial reductions of conic quadratic programming problems to linear programming problems in terms of Banach spaces.
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