Global optimization techniques for solving the general quadratic integer programming problem

We consider the problem of minimizing a general quadratic function over a polytope in the n-dimensional space with integrality restrictions on all of the variables. (This class of problems contains, e.g., the quadratic 0–1 program as a special case.) A finite branch and bound algorithm is established, in which the branching procedure is the so-called ‘integral rectangular partition’, and the bound estimation is performed by solving a concave programming problem with a special structure. Three methods for solving this special concave program are proposed.