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

Authors:
Jean-Philippe P. Richard;Ismael R. de Farias, Jr.;George L. Nemhauser
Affiliations:
-;-;-
Venue:
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Year:
2002

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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 superlinear 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.