We consider the general nonconvex quadratic programming problem and provide a series of convex positive semidefinite programs (or LMI relaxations) whose sequence of optimal values is monotone and converges to the optimal value of the original problem. It improves and includes as a special case the well-known Shor's LMI formulation. Often, the optimal value is obtained at some particular early relaxation as shown on some nontrivial test problems from Floudas and Pardalos (1990).
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