An alternative perspective on copositive and convex relaxations of nonconvex quadratic programs

Abstract We study convex relaxations of nonconvex quadratic programs. identify a family so-called feasibility preserving relaxations, which includes the well-known copositive and doubly nonnegative with property that relaxation is feasible if only program feasible. observe each in this implicitly induces underestimator objective function on region program. This alternative perspective enables us to establish several useful properties corresponding underestimators. In particular, recession cone does not contain any directions negative curvature, we show arising from precisely envelope program, strengthening Burer’s result exactness case also present an algorithmic recipe for constructing instances programs finite optimal value but unbounded rather large including relaxation.