  In this paper, we study some bounds for nonconvex quadratically constrained
quadratic programs. We propose two types of bounds for quadratically
constrained quadratic programs, quadratic and cubic bounds. For quadratic
bounds, we use affine functions as Lagrange multipliers. We demonstrate that
most semi-definite relaxations can be obtained as the dual of a quadratic
bound. In addition, we study bounds obtained by changing the ground set. For
cubic bounds, in addition to affine multipliers we employ quadratic functions.
We provide a comparison between the proposed cubic bound and typical bounds for
standard quadratic programs. Moreover, we report comparison results of a
quadratic and a cubic bound for some
  non-convex quadratically constrained quadratic programs.
