Skip to main content
Log in

The rank of (mixed-) integer polyhedra

  • Short Communication
  • Series A
  • Published:
Mathematical Programming Submit manuscript

Abstract

We define a purely geometrical notion of the rank of (mixed-) integer rational polyhedra that differs substantially from the existing notions found in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Cook W., Kannan R., Schrijver A.: Chvatal closures for mixed-integer programming problems. Math. Prog. 47, 155–174 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cornuejols G., Li Y.: On the rank of mixed 0–1 polyhedra. Math. Prog. 91, 391–397 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Nemhauser G., Wolsey L.: A recursive procedure to generate all cuts for 0–1 mixed integer programs. Math. Prog. 46, 379–390 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  4. Padberg M.W.: Linear Optimization and Extensions. 2nd edn. Springer, Berlin (1999)

    MATH  Google Scholar 

  5. Padberg, M.W.: Classical cuts for mixed-integer programming and branch-and-cut. Math. Meth. O.R. 53, 173–203 (2001), [reprinted in Ann. O.R. 139, 321–352 (2005)]

  6. Padberg M.W.: Mixed-integer programming—1968 and thereafter. Ann. O.R. 149, 163–175 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Padberg, M.W.: Facets and rank of integer polyhedra. Working paper, presented in preliminary form in a plenary session at the XVIth ISMP in August 1997 at the EPFL in Lausanne (Switzerland) under the title “Facets, Rank of Integer Polyhedra and Other Topics” (2011)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Manfred W. Padberg.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Padberg, M.W. The rank of (mixed-) integer polyhedra. Math. Program. 137, 593–599 (2013). https://doi.org/10.1007/s10107-011-0500-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10107-011-0500-0

Mathematics Subject Classification (2000)

Navigation