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Split Closure and Intersection Cuts

  • Kent Andersen
  • Gérard Cornuéjols
  • Yanjun Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2337)

Abstract

In the seventies, Balas introduced intersection cuts for a Mixed Integer Linear Program (MILP), and showed that these cuts can be obtained by a closed form formula from a basis of the standard linear programming relaxation. In the early nineties, Cook, Kannan and Schrijver introduced the split closure of an MILP, and showed that the split closure is a polyhedron. In this paper, we show that the split closure can be obtained using only intersection cuts. We give two different proofs of this result, one geometric and one algebraic. Furthermore, the result is used to provide a new proof of the fact that the split closure is a polyhedron. Finally, we extend the result to more general two-term disjunctions.

Keywords

Mixed Integer Linear Program Valid Inequality Early Ninety Closed Form Formula Split Closure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Balas, E.: Intersection cuts — a new type of cutting planes for integer programming. Operations Research 19 (1971) 19–39.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Balas, E.: Disjunctive programming. Annuals of Discrete Mathematics 5 (1979) 3–51.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Balas, E., Perregaard, M.: A precise correspondence between lift-and-project cuts, simple disjunctive cuts, and mixed integer Gomory cuts for 0-1 programming. Technical Report MSRR-631, GSIA, Carnegie Mellon University, 2000.Google Scholar
  4. 4.
    Cook, W., Kannan, R., Schrijver, A.: Chvátal closures for mixed integer programs. Mathematical Programming 47 (1990) 155–174.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Kent Andersen
    • 1
  • Gérard Cornuéjols
    • 1
  • Yanjun Li
    • 1
  1. 1.Graduate School of Industrial AdministrationCarnegie Mellon UniversityPittsburghUSA

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