Skip to main content
SpringerLink
Log in

Disjunctive Programming and Its Relation to Integer Programming

  • Chapter
  • First Online:
Disjunctive Programming

  • 1219 Accesses

Abstract

Disjunctive programming is optimization over disjunctive sets. A (linear) disjunctive set is the solution set of a system of (linear) inequalities joined by the logical connectives of conjunction (∧, “and”, juxtaposition), disjunction (∨, “or”), negation (¬, “complement of”).

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. E. Balas, Intersection cuts—a new type of cutting planes for integer programming. Operations Research, 19, 1971, 19–39.

    Article  MathSciNet  Google Scholar 

  2. E. Balas, Integer programming and convex analysis: intersection cuts from outer polars. Mathematical Programming, 2, 1972, 330–382.

    Article  MathSciNet  Google Scholar 

  3. E. Balas, Disjunctive Programming: Properties of the Convex Hull of Feasible Points. MSRR No. 348, Carnegie Mellon University, July 1974.

    Google Scholar 

  4. E. Balas, Disjunctive Programming: Cutting Planes from Logical Conditions. O.L. Mangasarian, R.R. Meyer and S.M. Robinson (editors). Nonlinear Programming 2, Academic Press, 1975, 279–312.

    Google Scholar 

  5. E. Balas, A Note on Duality in Disjunctive Programming. Journal of Optimization Theory and Applications, 21, 1977, 523–528.

    Article  MathSciNet  Google Scholar 

  6. E. Balas, Disjunctive Programming. Annals of Discrete Mathematics, 5, 1979, 3–51.

    Article  MathSciNet  Google Scholar 

  7. R. Gomory, Outline of an algorithm for integer solutions to linear programs. Bulletin of the American Mathematical Society 64, 1958, 275–278.

    Article  MathSciNet  Google Scholar 

  8. R. Gomory, An algorithm for the mixed integer problem. The RAND Corporation, 1960.

    Google Scholar 

  9. R. Gomory, Some polyhedra related to combinatorial problems. Linear Algebra and Its Applications, 2, 1969, 451–558.

    Article  MathSciNet  Google Scholar 

  10. P. Halmos. Naive Set Theory. Van Nostrand, 1960.

    Google Scholar 

  11. E. Johnson, The group problem for mixed integer programming. Math Programming Study 2, 1974, 137–179.

    Article  MathSciNet  Google Scholar 

  12. E. Mendelson, Introduction to Mathematical Logic. Van Nostrand, 1979.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA

    Egon Balas

Authors
  1. Egon Balas
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Balas, E. (2018). Disjunctive Programming and Its Relation to Integer Programming. In: Disjunctive Programming. Springer, Cham. https://doi.org/10.1007/978-3-030-00148-3_1

Download citation

Publish with us

Policies and ethics

Search

Navigation