We present the implementation of a branch-and-cut algorithm for bound constrained nonconvex quadratic programs. We use a class of inequalities developed in [12] as cutting planes. We present various branching strategies and compare the algorithm to several other methods to demonstrate its effectiveness.

The famous Padberg–Rao separation algorithm for b-matching polyhedra can be implemented to run in O(|V |2|E| log(|V |2/|E|)) time in the uncapacitated case, and in O(|V ||E|2 log (|V |2/|E|)) time in the capacitated case. We give a new and simple algorithm for the capacitated case which can be implemented to run in O(|V |2|E| log(|V |2/|E|)) time.

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Theorem 1 (Cheese Pizza Theorem). For a positive integer N, divide a pizza into 2N slices by choosing an arbitrary point P in the pizza and making N straight cuts through P, the cuts meeting to form 2N equal angles. Alternately color adjacent slices gray and white. Let O denote the center of the pizza. The total areas of gray and white will then satisfy the following. (a) When N ≥ 4 is even, th...