A branch-and-cut algorithm for Mixed-Integer Bilinear Programming

In this paper, we consider the Mixed-Integer Bilinear Programming problem, a widely-used reformulation of the classical mixed-integer quadratic programming problem. For this problem we describe a branch- and-cut algorithm for its exact solution, based on a new family of intersection cuts derived from bilinear- specific disjunctions. We also introduce a new branching rule that is specifically designed for bilinear problems. We computationally analyze the behavior of the proposed algorithm on a large set of mixed- integer quadratic instances from the MINLPlib problem library. Our results show that our method, even without intersection cuts, is competitive with a state-of-the-art mixed-integer nonlinear solver. As to intersection cuts, their extensive use at each branching node tends to slow down the solver for most problems in our test bed, but they are extremely effective for some specific instances.