Reducing the number of variables in integer quadratic programming problem

In this paper, a new variable reduction technique is presented for general integer quadratic programming problem (GP)(GP), under which some variables of (GP)(GP) can be fixed at zero without sacrificing optimality. A sufficient condition and a necessary condition for the identification of dominated terms are provided. By comparing the given data of the problem and the upper bound of the variables, if they meet certain conditions, some variables can be fixed at zero. We report a computational study to demonstrate the efficacy of the proposed technique in solving general integer quadratic programming problems. Furthermore, we discuss separable integer quadratic programming problems in a simpler and clearer form.