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On the Rank of Disjunctive Cuts

Author:

Alberto Del PiaAuthors Info & Claims

Mathematics of Operations Research, Volume 37, Issue 2

Pages 372 - 378

https://doi.org/10.1287/moor.1110.0527

Published: 01 May 2012 Publication History

Abstract

Let L be a family of lattice-free polyhedra in R^m containing the splits. Given a polyhedron P in R^{m + n}, we characterize when a valid inequality for P ∩ (Z^m × Rⁿ) can be obtained with a finite number of disjunctive cuts corresponding to the polyhedra in L. We also characterize the lattice-free polyhedra M such that all the disjunctive cuts corresponding to M can be obtained with a finite number of disjunctive cuts corresponding to the polyhedra in L for every polyhedron P. Our results imply interesting consequences, related to split rank and to integral lattice-free polyhedra, that extend recent research findings.

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Cited By

Dey SMolinaro M(2018)Theoretical challenges towards cutting-plane selectionMathematical Programming: Series A and B10.1007/s10107-018-1302-4170:1(237-266)Online publication date: 1-Jul-2018
https://dl.acm.org/doi/10.1007/s10107-018-1302-4
Averkov GKrümpelmann JWeltge S(2017)Notions of Maximality for Integral Lattice-Free PolyhedraMathematics of Operations Research10.1287/moor.2016.083642:4(1035-1062)Online publication date: 1-Nov-2017
https://dl.acm.org/doi/10.1287/moor.2016.0836
Bodur MDash SGünlük O(2017)Cutting planes from extended LP formulationsMathematical Programming: Series A and B10.1007/s10107-016-1005-7161:1-2(159-192)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1007/s10107-016-1005-7
Show More Cited By

Index Terms

On the Rank of Disjunctive Cuts
1. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image Mathematics of Operations Research

Mathematics of Operations Research Volume 37, Issue 2

05 2012

200 pages

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INFORMS

Linthicum, MD, United States

Publication History

Published: 01 May 2012

Received: 13 May 2011

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Cited By

Dey SMolinaro M(2018)Theoretical challenges towards cutting-plane selectionMathematical Programming: Series A and B10.1007/s10107-018-1302-4170:1(237-266)Online publication date: 1-Jul-2018
https://dl.acm.org/doi/10.1007/s10107-018-1302-4
Averkov GKrümpelmann JWeltge S(2017)Notions of Maximality for Integral Lattice-Free PolyhedraMathematics of Operations Research10.1287/moor.2016.083642:4(1035-1062)Online publication date: 1-Nov-2017
https://dl.acm.org/doi/10.1287/moor.2016.0836
Bodur MDash SGünlük O(2017)Cutting planes from extended LP formulationsMathematical Programming: Series A and B10.1007/s10107-016-1005-7161:1-2(159-192)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1007/s10107-016-1005-7
Conforti MDel Pia ADi Summa MFaenza Y(2015)Reverse split rankMathematical Programming: Series A and B10.1007/s10107-015-0883-4154:1-2(273-303)Online publication date: 1-Dec-2015
https://dl.acm.org/doi/10.1007/s10107-015-0883-4
Dash SDobbs NGünlük ONowicki TŚwirszcz G(2014)Lattice-free sets, multi-branch split disjunctions, and mixed-integer programmingMathematical Programming: Series A and B10.1007/s10107-013-0654-z145:1-2(483-508)Online publication date: 1-Jun-2014
https://dl.acm.org/doi/10.1007/s10107-013-0654-z
Conforti MDel Pia A(2014)Disjunctive programming and relaxations of polyhedraMathematical Programming: Series A and B10.1007/s10107-013-0634-3144:1-2(307-314)Online publication date: 1-Apr-2014
https://dl.acm.org/doi/10.1007/s10107-013-0634-3

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