Global Optimality Conditions for Quadratic Optimization Problems with Binary Constraints

We consider nonconvex quadratic optimization problems with binary constraints. Our main result identifies a class of quadratic problems for which a given feasible point is global optimal. We also establish a necessary global optimality condition. These conditions are expressed in a simple way in terms of the problem’s data. We also study the relations between optimal solutions of the nonconvex binary quadratic problem versus the associated relaxed and convex problem defined over the l∞ norm. Our approach uses elementary arguments based on convex duality.