On the relationship between standard intersection cuts, lift-and-project cuts, and generalized intersection cuts

Balas, E and Kis, Tamás (2016) On the relationship between standard intersection cuts, lift-and-project cuts, and generalized intersection cuts. MATHEMATICAL PROGRAMMING, 160. pp. 85-114. ISSN 0025-5610 10.1007/s10107-015-0975-1

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Abstract

We examine the connections between the classes of cuts in the title. We show that lift-and-project (L&P) cuts from a given disjunction are equivalent to generalized intersection cuts from the family of polyhedra obtained by taking positive combinations of the complements of the inequalities of each term of the disjunction. While L&P cuts from split disjunctions are known to be equivalent to standard intersection cuts (SICs) from the strip obtained by complementing the terms of the split, we show that L&P cuts from more general disjunctions may not be equivalent to any SIC. In particular, we give easily verifiable necessary and sufficient conditions for a L&P cut from a given disjunction D to be equivalent to a SIC from the polyhedral counterpart of D. Irregular L&P cuts, i.e. those that violate these conditions, have interesting properties. For instance, unlike the regular ones, they may cut off part of the corner polyhedron associated with the LP solution from which they are derived. Furthermore, they are not exceptional: their frequency exceeds that of regular cuts. A numerical example illustrates some of the above properties. © 2016 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society

Item Type: Article
Uncontrolled Keywords: Lift-and-project; Intersection cut; Generalized intersection; GEOMETRY; Lift-and-project cuts; Intersection cuts; Integer programming; Generalized intersection cuts; Corner polyhedra
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Divisions: Research Laboratory on Engineering & Management Intelligence
SWORD Depositor: MTMT Injector
Depositing User: MTMT Injector
Date Deposited: 13 Jan 2017 14:49
Last Modified: 13 Jan 2017 14:49
URI: http://eprints.sztaki.hu/id/eprint/8898

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