Skip to main content
Log in

Optimization with an approximate Lagrangian

  • Published:
Mathematical Programming Submit manuscript

Abstract

An error analysis is provided for discrete Lagrangian cell problems where the exact objective function for each cell is approximated by a simpler expression. Easily-calculated rigorous and heuristic bounds are given for the error in the value of the objective function. The solution itself, however, can be significantly distorted.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. Charnes and W.W. Cooper, “A note on the ‘Fail-Safe’ properties of the ‘Generalized Lagrange Multiplier Method’”, and H. Everett, “Comment on preceeding note”,Operations Research 13 (1965) 674–678.

    Google Scholar 

  2. Richard H. Day, “Allocating weapons to target complexes by means of nonlinear programming”,Operations Research 14 (1966) 992–1013.

    Google Scholar 

  3. H. Everett, III, “Generalized Lagrange multiplier method for solving problems of optimum allocation of resources”,Operations Research 11 (1963) 399–417.

    Google Scholar 

  4. G.G. Furman and H.J. Greenberg, “Optimal weapon allocation with overlapping area defenses”,Operations Research 21 (1973) 1291–1308.

    Google Scholar 

  5. S. Kaplan, “Solution of the Lorie—Savage and similar integer programming problems by the generalized Lagrange multiplier method”,Operations Research 14 (1966) 1130–1136.

    Google Scholar 

  6. F. Lemus and K.H. David, “An optimum allocation of different weapons to a target complex”,Operations Research 11 (1963) 787–794.

    Google Scholar 

  7. E.P. Loane, “An algorithm to solve finite separable single-constrained optimization problems”,Operations Research 19 (1971) 1477–1493.

    Google Scholar 

  8. G.J. Silverman, “Primal decomposition of mathematical programs by resource allocation — I and II”,Operations Research 20 (1972) 58–93.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schweitzer, P.J. Optimization with an approximate Lagrangian. Mathematical Programming 7, 191–198 (1974). https://doi.org/10.1007/BF01585515

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01585515

Keywords