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We consider the NP-hard problem of minimizing a convex quadratic functionover the integer lattice ${\bf Z}^n$. We present a simple semidefiniteprogramming (SDP) relaxation for obtaining a nontrivial lower bound on theoptimal value of the problem. By interpreting the solution to the SDPrelaxation probabilistically, we obtain a randomized algorithm for finding goodsuboptimal solutions, and thus an upper bound on the optimal value. Theeffectiveness of the method is shown for numerical problem instances of varioussizes.

A Semidefinite Programming Method for Integer Convex Quadratic Minimization