Technical Note—Converting the 0-1 Polynomial Programming Problem to a 0-1 Linear Program

Abstract

Rules are given that permit 0-1 polynomial programming problems to be converted to 0-1 linear programming problems in a manner that replaces cross-product terms by continuous rather than integer variables. Since the difficulty of mixed integer programming problems often depends more strongly on the number of integer variables than on the number of continuous variables, such rules are expected to have advantages in practical applications. In addition, the continuous variables automatically receive integer values, and hence our formulation can also be exploited by methods designed to take advantage of a pure integer structure.