A Semidefinite Programming Method for Integer Convex Quadratic Minimization

@article{Park2018ASP,
  title={A Semidefinite Programming Method for Integer Convex Quadratic Minimization},
  author={Jaehyun Park and Stephen Boyd},
  journal={Optimization Letters},
  year={2018},
  volume={12},
  pages={499-518}
}
We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice Z. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the problem. By interpreting the solution to the SDP relaxation probabilistically, we obtain a randomized algorithm for finding good suboptimal solutions, and thus an upper bound on the optimal value. The effectiveness of the method is shown for numerical problem… CONTINUE READING