Cardinality constrained Boolean quadratic polytope Original Research Article

We study the polyhedral structure of an integer programming formulation of the cardinality constrained Boolean quadratic problem. We give many facet-defining inequalities. The separation problems for these inequalities appear to be difficult, which explains, in part, the difficulty encountered in solving these problems via a branch-and-cut methodology. As a special case of these inequalities, we obtain some previously known inequalities for the equipartition problem.