### 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.

Original language | English (US) |
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Pages (from-to) | 161-175 |

Number of pages | 15 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 2337 LNCS |

State | Published - Dec 1 2002 |

Externally published | Yes |

Event | 9th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2002 - Cambridge, MA, United States Duration: May 27 2002 → May 29 2002 |

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## Cite this

Richard, J. P. P., De Farias, I. R., & Nemhauser, G. L. (2002). Lifted inequalities for 0-1 mixed integer programming: Basic theory and algorithms.

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,*2337 LNCS*, 161-175.