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Cutting planes for RLT relaxations of mixed 0-1 polynomial programs

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>2015
<mark>Journal</mark>Mathematical Programming
Issue number2
Volume151
Number of pages20
Pages (from-to)639–658
Publication statusPublished
Early online date23/01/15
Original languageEnglish

Abstract

The Reformulation-Linearization Technique (RLT), due to Sherali and Adams, can be used to construct hierarchies of linear programming relaxations of mixed 0-1 polynomial programs. As one moves up the hierarchy, the relaxations grow stronger, but the number of variables increases exponentially. We present a procedure that generates cutting planes at any given level of the hierarchy, by optimally weakening linear inequalities that are valid at any given higher level. Computational experiments, conducted on instances of the quadratic knapsack problem, indicate that the cutting planes can close a significant proportion of the integrality gap.