  The Johnson-Lindenstrauss lemma allows dimension reduction on real vectors
with low distortion on their pairwise Euclidean distances. This result is often
used in algorithms such as $k$-means or $k$ nearest neighbours since they only
use Euclidean distances, and has sometimes been used in optimization algorithms
involving the minimization of Euclidean distances. In this paper we introduce a
first attempt at using this lemma in the context of feasibility problems in
linear and integer programming, which cannot be expressed only in function of
Euclidean distances.
