@article{Buchheim_De Santis_Palagi_Piacentini_2012, title={An Exact Algorithm for Quadratic Integer Minimization using Nonconvex Relaxations}, volume={4}, url={https://rosa.uniroma1.it/rosa00/index.php/dis_technical_reports/article/view/10023}, abstractNote={We propose a branch-and-bound algorithm for minimizing a not necessarily convex quadratic function over integer variables. The algorithm is based on lower bounds computed as continuous minima of the objective function over appropriate ellipsoids. In the nonconvex case, we use ellipsoids enclosing the feasible region of the problem. In spite of the nonconvexity, these minima can be computed quickly. We present several ideas that allow to accelerate the solution of the continuous relaxation within a branch-and-bound scheme and examine the performance of the overall algorithm by computational experiments.}, number={5}, journal={Department of Computer and System Sciences Antonio Ruberti Technical Reports}, author={Buchheim, Christoph and De Santis, Marianna and Palagi, Laura and Piacentini, Mauro}, year={2012}, month={Jun.}, pages={29} }