Numerical Experience with Lower Bounds for MIQP Branch-And-Bound

The solution of convex mixed-integer quadratic programming (MIQP) problems with a general branch-and-bound framework is considered. It is shown how lower bounds can be computed efficiently during the branch-and-bound process. Improved lower bounds such as the ones derived in this paper can reduce the number of quadratic programming (QP) problems that have to be solved. The branch-and-bound approach is also shown to be superior to other approaches in solving MIQP problems. Numerical experience is presented which supports these conclusions.