Skip to main content
SpringerLink
Log in

Lagrangean Relaxation Revisited, Technical Note

  • Published:
Constraints Aims and scope Submit manuscript

Abstract

In this paper we consider some theoretical aspects of Lagrangean relaxation which do not seem to appear explicitly in the literature, and add a little more explicit completeness to this area. These concern three key constructs, \(\left\{ {v(IP),v(\overline {IP} ),v(DP)} \right\}\) and associated optimality, duality and feasibility aspects of Lagrangean relaxation.

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. M.S. Bazaraa and J.J. Goode (1979) A Survey of Various Tactics for Generating Lagrangian Multipliers in the Context of Lagrangian Duality, European Journal of Operational Research 3: 322–338.

    Google Scholar 

  2. H. Everett, III (1963) Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources, Operations Research 11: 399–417.

    Google Scholar 

  3. M.L. Fisher (1981) Lagrangian Method for Solving Integer Programming Problems, Management Science 27: 1–18.

    Google Scholar 

  4. M.L. Fisher (1985) An Applications Oriented Guide to Lagrangian Relaxation, Interfaces 15: 10–21

    Google Scholar 

  5. A.M. Geoffrion (1974) Lagrangean Relaxation for Integer Programming, Mathematical Programming Study 2: 82–114.

    Google Scholar 

  6. M. Held and R.M. Karp (1970) The Travelling Salesman Problem and Minimum Spanning Trees, Operations Research 18: 1138–1162.

    Google Scholar 

  7. O.L. Mangasarian (1969) Nonlinear Programming, McGraw Hill, New York.

    Google Scholar 

  8. G.L. Nemhauser and L.A. Wolsey (1988) Integer and combinatorial Optimisation, J. Wiley & Sons, Inc., Chichester.

    Google Scholar 

  9. G.L. Nemhauser and Z. Ullman (1968) A Note on the Generalized Lagrange Multiplier Solution to an Integer Programming Problem, Operations Research, 450–452.

  10. J.F. Shapiro (1979) A Survey of Lagrangean Techniques for Discrete Optimisation, Annals of Discrete Mathematics 5: 113–138.

    Google Scholar 

  11. J. Stoer and C. Witzgall (1970) Convexity and Optimisation in Finite Dimensions I, Springer Verlag, Berlin.

    Google Scholar 

  12. W.I. Zangwill (1969) Nonlinear Programming, Prentice Hall Inc. Englewood Cliffs, N.J.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Manchester, England

    D.J. White

Authors
  1. D.J. White
    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

White, D. Lagrangean Relaxation Revisited, Technical Note. Constraints 4, 67–77 (1999). https://doi.org/10.1023/A:1009897727677

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009897727677

Keywords

Search

Navigation