The use of random projections in mathematical programming allows standard solution algorithms to solve instances of much larger sizes, at least approximately. Approximation results have been derived in the relevant literature for many specific problems, as well as for several mathematical programming subclasses. Despite the theoretical developments, it is not always clear that random projections are actually useful in solving mathematical programs in practice. In this paper we provide a computational assessment of the application of random projections to linear programming.

Abstract We consider polyhedral separation of sets as a possible tool in supervised classification. In particular, we focus on the optimization model introduced by Astorino and Gaudioso (J Optim Theory Appl 112(2):265–293, 2002) and adopt its reformulation in difference of convex (DC) form. We tackle the problem by adapting the algorithm for DC programming known as DCA. We present the results of the implementation of DCA on a number of benchmark classification datasets.