Skip to main content
SpringerLink
Log in

On the complexity of the surrogate dual of 0–1 programming

  • Published:
Zeitschrift für Operations Research Aims and scope Submit manuscript

Abstract

It is shown that the surrogate dual of a 0–1 programming problem can be solved by 0(m 3) knapsack calls, ifm denotes the number of constraints.

Zusammenfassung

Es wird gezeigt, daß das “surrogate duale” Problem zu einer linearen Optimierungsaufgabe mit binären Variablen durch 0(m 3) Rucksackprobleme gelöst werden kann. Dabei bezeichnetm die Anzahl der Nebenbedingungen.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Balas E (1967) Discrete programming by the filter method. Opns Res 15:915–957

    Google Scholar 

  2. Bland RG, Goldfarb D, Todd MJ (1981) The ellipsoid method: a survey. Opns Res 29: 1039–1091

    Google Scholar 

  3. Boros E (1984) The surrogate dual problem. Working paper, Computer and Automation Institute, Hungarian Academy of Sciences MO/53, (in Hungarian)

  4. Dyer ME (1980) Calculating surrogate constraints. Math Prog 19:255–278

    Article  Google Scholar 

  5. Gacs P, Lovász L (1979) Khachian's algorithm for linear programming. Research Report, Computer Science Dep., Stanford Univ.

  6. Geoffrion AM (1969) An improved implicit enumeration approach for integer programming. Opns Res 17:437–454

    Google Scholar 

  7. Glover F (1965) A multiphase-dual algorithm for the zero-one integer programming problem. Opns Res 13:879–919

    Google Scholar 

  8. Glover F (1968) Surrogate constraints. Opns Res 16:741–749

    Google Scholar 

  9. Glover F (1975) Surrogate constraint duality in mathematical programming. Opns Res 23: 434–451

    Google Scholar 

  10. Greenberg HJ, Pierskalla WP (1970) Surrogate mathematical programming. Opns Res 18: 924–939

    Google Scholar 

  11. Greenberg HJ, Pierskalla WP (1973) Quasi-conjugate functions and surrogate duality. Cahiers du Centre d'Etudes de Recherche Operationelle 15:437–440

    Google Scholar 

  12. Grotschel M, Lovasz L, Schrijver A (1981) The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1:169–197

    Google Scholar 

  13. Karwan MH, Rardin RL (1979) Some relationships between lagrangean and surrogate duality in integer programming. Math Prog 17:320–334

    Article  Google Scholar 

  14. Karwan MH, Rardin RL (1980) Searchability of the composite and multiple surrogate dual functions. Opns Res 28:1251–1257

    Google Scholar 

  15. Khachiyan LG (1979) A polynomial algorithm in linear programming. Doklady Akademiia Nauk SSSR 224:1093–1096 (translated in Soviet Mathematics Doklady 20:191–194 (1979))

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer and Automation Institute, Hungarian Academcy of Sciences, Kende u. 13-17, H-1502, Budapest XI

    Endre Boros

Authors
  1. Endre Boros
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boros, E. On the complexity of the surrogate dual of 0–1 programming. Zeitschrift für Operations Research 30, A145–A153 (1986). https://doi.org/10.1007/BF01919175

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01919175

Key words

Search

Navigation