Lifted Inequalities for 0-1 Mixed Integer Programming: Basic Theory and Algorithms

Abstract

We study the mixed 0-1 knapsack polytope, which is defined by a single knapsack constraint that contains 0-1 and bounded continuous variables. We develop a lifting theory for the continuous variables. In particular, we present a pseudo-polynomial algorithm for the sequential lifting of the continuous variables. We introduce the concept of super-linear inequalities and show that our lifting scheme can be significantly simplified for them. Finally, we show that superlinearity results can be generalized to nonsuperlinear inequalities when the coefficients of the continuous variables lifted are large.