Gap inequalities for non-convex mixed-integer quadratic programs

Laurent and Poljak introduced a very general class of valid linear inequalities, called gap inequalities, for the max-cut problem. We show that an analogous class of inequalities can be defined for general non-convex mixed-integer quadratic programs. These inequalities dominate some inequalities arising from a natural semidefinite relaxation.

► The gap inequalities form a very general class of cutting planes for the max-cut problem.
► We extend them to the case of non-convex mixed-integer quadratic programs.
► Our inequalities dominate some inequalities arising from a natural semidefinite relaxation.