Globally Solving Nonconvex Quadratic Programs via Linear Integer Programming Techniques

A quadratic program (QP) is a well-studied fundamental NP-hard optimization problem which optimizes a quadratic objective over a set of linear constraints. In this paper, we reformulate QPs as a mixed-integer linear problem (MILP). This is done via the reformulation of QP as a linear complementary problem, and the use of binary variables together with some fundamental results on the solution of perturbed linear systems, to model the complementary constraints. Reformulating non-convex QPs as MILPs provides an advantageous way to obtain global solutions as it allows to use current state-of-the-art MILP solvers. To illustrate, we compare the performance of our solution approach with the current benchmark global QP solver quadprogBB on a large variety of QP test instances. The MATLAB code, called quadprogIP, and the instances used to perform these numerical experiments are publicly available at this https URL