Global optimality conditions for quadratic optimization problems with binary constraints

We consider nonconvex quadratic optimization problems with binary constrain ts. Our main result identifies a class of quadratic problems for which a gi ven feasible point is global optimal. We also establish a necessary global optimality condition. These conditions are expressed in a simple way in ter ms of the problem's data. We also study the relations between optimal solut ions of the nonconvex binary quadratic problem versus the associated relaxe d and convex problem defined over the l(infinity) norm. Our approach uses e lementary arguments based on convex duality.