Sequence Independent Lifting in Mixed Integer Programming

Zonghao Gu, George L. Nemhauser and Martin W.P. Savelsbergh
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Zonghao Gu: Georgia Institute of Technology
George L. Nemhauser: Georgia Institute of Technology
Martin W.P. Savelsbergh: Georgia Institute of Technology

Journal of Combinatorial Optimization, 2000, vol. 4, issue 1, No 6, 109-129

Abstract: Abstract We investigate lifting, i.e., the process of taking a valid inequality for a polyhedron and extending it to a valid inequality in a higher dimensional space. Lifting is usually applied sequentially, that is, variables in a set are lifted one after the other. This may be computationally unattractive since it involves the solution of an optimization problem to compute a lifting coefficient for each variable. To relieve this computational burden, we study sequence independent lifting, which only involves the solution of one optimization problem. We show that if a certain lifting function is superadditive, then the lifting coefficients are independent of the lifting sequence. We introduce the idea of valid superadditive lifting functions to obtain good aproximations to maximum lifting. We apply these results to strengthen Balas' lifting theorem for cover inequalities and to produce lifted flow cover inequalities for a single node flow problem.

Keywords: integer programming; lifting (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (24)

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DOI: 10.1023/A:1009841107478

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