Skip to main content
SpringerLink
Log in
Book cover

Encyclopedia of Optimization pp 1847–1851Cite as

Least-index Anticycling Rules

LindAcR

  • Reference work entry

Article Outline

Keywords

Consistent Labeling For the Max-Flow Problem

Linear Optimization

  Least-Index Rules for Feasibility Problem

  The Linear Optimization Problem

  Least-Index Pivoting Methods for LO

Linear Complementarity Problems

Least-Index Rules and Oriented Matroids

See also

References

This is a preview of subscription content, 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   2,500.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   2,499.99
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

Learn about institutional subscriptions

References

  1. Avis D, Chvátal V (1978) Notes on Bland's rule. Math Program Stud 8:24–34

    Google Scholar 

  2. Beale EML (1955) Cycling in the dual simplex algorithm. Naval Res Logist Quart 2:269–275

    Article  MathSciNet  Google Scholar 

  3. Bjorner A, Las Vergnas M, Sturmfels B, White N, Ziegler G (1993) Oriented matroids. Cambridge Univ. Press, Cambridge

    Google Scholar 

  4. Bland RG (1977) A combinatorial abstraction of linear programming. J Combin Th B 23:33–57

    Article  MathSciNet  MATH  Google Scholar 

  5. Bland RG (1977) New finite pivoting rules for the simplex method. Math Oper Res 2:103–107

    MathSciNet  MATH  Google Scholar 

  6. Chang YY (1979) Least index resolution of degeneracy in linear complementarity problems. Techn Report Dept Oper Res Stanford Univ 79-14

    Google Scholar 

  7. Chang YY, Cottle RW (1980) Least index resolution of degeneracy in quadratic programming. Math Program 18:127–137

    Article  MathSciNet  MATH  Google Scholar 

  8. Cottle R, Pang JS, Stone RE (1992) The linear complementarity problem. Acad. Press, New York

    MATH  Google Scholar 

  9. Dantzig GB (1963) Linear programming and extensions. Princeton Univ. Press, Princeton

    MATH  Google Scholar 

  10. Farkas J (1902) Theorie der Einfachen Ungleichungen. J Reine Angew Math 124:1–27

    Google Scholar 

  11. Ford LR Jr, Fulkerson DR (1962) Network flows. Princeton Univ. Press, Princeton

    Google Scholar 

  12. Fukuda K (1982) Oriented matroid programming. PhD Thesis Waterloo Univ.

    Google Scholar 

  13. Fukuda K, Namiki M (1994) On extremal behaviors of Murty's least index method. Math Program 64:365–370

    Article  MathSciNet  Google Scholar 

  14. Fukuda K, Terlaky T (1997) Criss-cross methods: A fresh view on pivot algorithms. In: Mathematical Programming, (B) Lectures on Mathematical Programming, ISMP97, vol 79. Lausanne, pp 369–396

    Google Scholar 

  15. Hall J, McKinnon KI (1998) A class of cycling counter-examples to the EXPAND anti-cycling procedure. Techn. Report Dept. Math. and Statist. Univ. Edinburgh

    Google Scholar 

  16. Den Hertog D, Roos C, Terlaky T (1993) The linear complementarity problem, sufficient matrices and the criss-cross method. LAA 187:1–14

    MathSciNet  MATH  Google Scholar 

  17. Hoffman AJ (1953) Cycling in the simplex method. Techn Report Nat Bureau Standards 2974

    Google Scholar 

  18. Klafszky E, Terlaky T (1989) Variants of the Hungarian method for solving linear programming problems. Math Oper Statist Ser Optim 20:79–91

    MathSciNet  MATH  Google Scholar 

  19. Klafszky E, Terlaky T (1991) The role of pivoting in proving some fundamental theorems of linear algebra. LAA 151:97–118

    MathSciNet  MATH  Google Scholar 

  20. Klafszky E, Terlaky T (1992) Some generalizations of the criss-cross method for quadratic programming. Math Oper Statist Ser Optim 24:127–139

    MathSciNet  MATH  Google Scholar 

  21. Klee V, Minty GJ (1972) How good is the simplex algorithm? In: Shisha O (ed) Inequalities-III. Acad. Press, New York, pp 1159–1175

    Google Scholar 

  22. Murty KG (1974) A note on a Bard type scheme for solving the complementarity problem. Oper Res 11(2–3):123–130

    MathSciNet  Google Scholar 

  23. Murty KG (1988) Linear complementarity, linear and nonlinear programming. Heldermann, Berlin

    MATH  Google Scholar 

  24. Murty KG (1992) Network programming. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  25. Roos C (1990) An exponential example for Terlaky's pivoting rule for the criss-cross simplex method. Math Program 46:78–94

    Article  MathSciNet  Google Scholar 

  26. Terlaky T (1985) A convergent criss-cross method. Math Oper Statist Ser Optim 16(5):683–690

    MathSciNet  MATH  Google Scholar 

  27. Terlaky T, Zhang S (1993) Pivot rules for linear programming: A survey on recent theoretical developments. Ann Oper Res 46:203–233

    Article  MathSciNet  Google Scholar 

  28. Tucker A (1977) A note on convergence of the Ford–Fulkerson flow algorithm. Math Oper Res 2(2):143–144

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department Comput. & Software, McMaster University, West Hamilton, Canada

    Tamás Terlaky

Authors
  1. Tamás Terlaky
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Terlaky, T. (2008). Least-index Anticycling Rules . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_327

Download citation

Publish with us

Policies and ethics

Search

Navigation