A note on solving quadratic programs using mixed-integer programming

Abstract

It is well-known that quadratic programs can be solved with linear programming-based algorithms utilizing Kuhn-Tucker optimality conditions. However, due to certain linear complementary conditions, these algorithms require a specialized simplex code with modified rules for basis entry. In this paper we show that these linear complementary conditions can be enforced via a mixed-integer formulation of the quadratic programming problem. This formulation may be solved using any general purpose mixed-integer programming code.