Equivalent formulations of nonlinear integer problems for efficient optimization

The linearization technique of Glover, which seems to be the most efficient one appearing in the literature, requires the addition of n new continuous variables (unconstrained in sign) and 4n new linear constraints to equivalently represent a 0-1 ‘quadratic’ integer problem with n variables. This paper shows that it is still possible to improve such a procedure. In fact, the number of new continuous variables can be kept at n (but constrained in sign) while further reducing the number of new linear constraints from 4n to 2n.