Skip to main content
SpringerLink
Log in
Book cover

Encyclopedia of Optimization pp 890–899Cite as

Ellipsoid Method

  • Reference work entry

Article Outline

Keywords

Abstract

Introduction

Method

  The Basic Ellipsoid Algorithm

  Polynomially Running Time: Avoiding the Assumptions

  Modifications

Applications

  Linear Programming

  Separation and Optimization

Conclusion

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. Padberg MW, Rao MR (1980) The Russian Method for Linear Inequalities. Graduate School of Business Administration, New York University, New York

    Google Scholar 

  2. Bland RG, Goldfarb D, Todd MJ (1981) The Ellipsoid Method: A Survey. Operat Res 29(6):1039–1091

    MATH  MathSciNet  Google Scholar 

  3. Garey MR, Johnson DS (1979) Computers and Intractability, A guide to the Theory of NP-Completeness. In: Klee V (ed) A series of books in the mathematical sciences. WH Freeman and Company, New York

    Google Scholar 

  4. Gács P, Lovász L (1981) Khachiyan's Algorithm for Linear Programming. Math Program Stud 14:61–68

    MATH  Google Scholar 

  5. Grötschel M, Lovász L, Schrijver A (1981) The Ellipsoid Method and Its Consequences in Combinatorial Optimization. Comb 1:169–197

    Google Scholar 

  6. Grötschel M, Lovász L, Schrijver A (1988) Geometric Algorithms and Combinatorial Optimization. In: Algorithms and Combinatorics 2. Springer, Berlin

    Google Scholar 

  7. Gill PE, Murray W, Saunders MA (1975) Methods for Computing and Modifying the LDV Factors of a Matrix. Math Comput 29(132):1051–1077

    Article  MATH  MathSciNet  Google Scholar 

  8. Gerards AMH, Schrijver A (1986) Matrices with the Edmonds-Johnson property. Comb 6(4):365–379

    MATH  MathSciNet  Google Scholar 

  9. Goldfarb D, Todd MJ (1982) Modifications and Implementation of The Ellipsoid Algorithm for Linear Programming. Math Program 23:1–19

    Article  MATH  MathSciNet  Google Scholar 

  10. Karmarkar N (1984) A New Polynomial-Time Algorithm for Linear Programming. Comb 4(4):373–395

    MATH  MathSciNet  Google Scholar 

  11. Khachiyan LG (1979) A Polynomial Algorithm in Linear Programming. Dokl Akad Nauk SSSR 244:1093–1096 (English translation: Sov Math Dokl, 20(1):191–194, 1979)

    Google Scholar 

  12. Khachiyan LG (1980) Polynomial Algorithms in Linear Programming. Zhurnal Vychislit Math Math Fiz 20:51–68 (English translation: USSR Comput Math Math Phys, 20(1):53–72, 1980)

    Google Scholar 

  13. Klee V, Minty GL (1972) How good is the Simplex Algorithm? Inequalities III. In: Shisha O (ed). Academic Press, New York, pp 159–175

    Google Scholar 

  14. Krol J, Mirman B (1980) Some Practical Modifications of The Ellipsoid Method for LP Problems. Arcon Inc, Boston

    Google Scholar 

  15. Lawler EL (1980) The Great Mathematical Sputnik of 1979. Science 20(7):12–15, 34–35

    Google Scholar 

  16. Murray W, Todd M (2005) Tributes to George Dantzig and Leonid Khachiyan. SIAM Act Group Optim – Views News 16(1–2):1–6

    Google Scholar 

  17. Nemhauser GL, Wolsey LA (1999) Integer and Combinatorial Optimization. In: Wiley-Interscience Series in Discret Mathematics and Optimization. Wiley, New York

    Google Scholar 

  18. Rebennack S (2006) Maximum Stable Set Problem: A Branch & Cut Solver. Diplomarbeit, Ruprecht–Karls Universität Heidelberg

    Google Scholar 

  19. Schrader R (1983) The Ellipsoid Method and Its Implications. OR Spektrum 5(1):1–13

    Article  MATH  Google Scholar 

  20. Shor NZ (1977) Cut-off Method with Space Extension in Convex Programming Problems. Kibern 13(1):94–95 (English translation: Cybern 13(1):94–96, 1977)

    Google Scholar 

  21. Khachiyan L (2005) 1952–2005: An Appreciation. SIAM News 38(10)

    Google Scholar 

  22. Tardos E (1986) A Strongly Polynomial Algorithm to Solve Combinatorial Linear Programs. Oper Res 34(2):250–256

    MATH  MathSciNet  Google Scholar 

  23. Tee GJ (1980) Khachian's efficient algorithm for linear inequalities and linear programming. SIGNUM Newsl 15(1):13–15

    Article  Google Scholar 

  24. Yudin DB, Nemirovski AS (1976) Evaluation of the Informational Complexity of Mathematical Programming Problems. Èkon Math Metod 12:128–142 (English translation: Matekon, 13(2):3–25, 1976–7)

    Google Scholar 

  25. Yudin DB, Nemirovski AS (1976) Informational Complexity and Efficient Methods for the Solution of Convex Extremal Problems. Èkon Math Metod 12:357–369 (English translation: Matekon, 13(3):25–45, 1977)

    Google Scholar 

  26. Yudin DB, Nemirovski AS (1977) Optimization Methods Adapting to the “Significant” Dimension of the Problem. Autom Telemekhanika 38(4):75–87 (English translation: Autom Remote Control, 38(4):513–524, 1977)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center of Applied Optimization, University of Florida, Gainesville, USA

    Steffen Rebennack

Authors
  1. Steffen Rebennack
    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

Rebennack, S. (2008). Ellipsoid Method . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_157

Download citation

Publish with us

Policies and ethics

Search

Navigation