Global solutions of nonconvex standard quadratic programs via mixed integer linear programming reformulations

Abstract A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) form over the unit simplex. We focus on reformulating as mixed integer linear programming problem. propose two alternative formulations. Our first formulation based casting with complementarity constraints. then employ binary variables to linearize For second formulation, we derive overestimating function objective and establish its tightness at any global minimizer. using obtain our formulation. both formulations, set valid inequalities. extensive computational results illustrate proposed reformulations significantly outperform other solution approaches. On larger instances, usually observe improvements several orders magnitude.